Question

Sin A/1+cosA=cosecA-cot A prove it plzz

Answer 1

Answer:

LHS = cosecA - cotA

        = 1/sinA - cosA/sinA

        = (1 - cosA)/sinA

On Rationalising we get,

= (1 - cosA)/sinA * (1 + cosA)/(1 + cosA)

= sin^2A/sinA(1 + cosA)

= sinA/(1+ cosA) = RHS

Hence Proved.  

✨Hope it will help you.✨

Answer 2

in these type of question first observe what we have and what we need

in these type of question first observe what we have and what we needwe are given with sin and cos terms and we need answer in cosec and cot term so we will first multiply and divide by 1-cosA

in these type of question first observe what we have and what we needwe are given with sin and cos terms and we need answer in cosec and cot term so we will first multiply and divide by 1-cosAwe get sinA*(1-cosA)/(1+cosA)*(1-cosA)

in these type of question first observe what we have and what we needwe are given with sin and cos terms and we need answer in cosec and cot term so we will first multiply and divide by 1-cosAwe get sinA*(1-cosA)/(1+cosA)*(1-cosA)now open all the brackets and we get

in these type of question first observe what we have and what we needwe are given with sin and cos terms and we need answer in cosec and cot term so we will first multiply and divide by 1-cosAwe get sinA*(1-cosA)/(1+cosA)*(1-cosA)now open all the brackets and we getsinA-sinA.cosA/1-cos^2A

in these type of question first observe what we have and what we needwe are given with sin and cos terms and we need answer in cosec and cot term so we will first multiply and divide by 1-cosAwe get sinA*(1-cosA)/(1+cosA)*(1-cosA)now open all the brackets and we getsinA-sinA.cosA/1-cos^2Awe can further simplify it as

in these type of question first observe what we have and what we needwe are given with sin and cos terms and we need answer in cosec and cot term so we will first multiply and divide by 1-cosAwe get sinA*(1-cosA)/(1+cosA)*(1-cosA)now open all the brackets and we getsinA-sinA.cosA/1-cos^2Awe can further simplify it assinA-sinAcosA/sin^2A

in these type of question first observe what we have and what we needwe are given with sin and cos terms and we need answer in cosec and cot term so we will first multiply and divide by 1-cosAwe get sinA*(1-cosA)/(1+cosA)*(1-cosA)now open all the brackets and we getsinA-sinA.cosA/1-cos^2Awe can further simplify it assinA-sinAcosA/sin^2Ausing identity(1-cos^2A=sin^2A)

in these type of question first observe what we have and what we needwe are given with sin and cos terms and we need answer in cosec and cot term so we will first multiply and divide by 1-cosAwe get sinA*(1-cosA)/(1+cosA)*(1-cosA)now open all the brackets and we getsinA-sinA.cosA/1-cos^2Awe can further simplify it assinA-sinAcosA/sin^2Ausing identity(1-cos^2A=sin^2A)now just divide both the terms by sin^2A

in these type of question first observe what we have and what we needwe are given with sin and cos terms and we need answer in cosec and cot term so we will first multiply and divide by 1-cosAwe get sinA*(1-cosA)/(1+cosA)*(1-cosA)now open all the brackets and we getsinA-sinA.cosA/1-cos^2Awe can further simplify it assinA-sinAcosA/sin^2Ausing identity(1-cos^2A=sin^2A)now just divide both the terms by sin^2Awe get (1/sinA)-(cosA/sinA)

in these type of question first observe what we have and what we needwe are given with sin and cos terms and we need answer in cosec and cot term so we will first multiply and divide by 1-cosAwe get sinA*(1-cosA)/(1+cosA)*(1-cosA)now open all the brackets and we getsinA-sinA.cosA/1-cos^2Awe can further simplify it assinA-sinAcosA/sin^2Ausing identity(1-cos^2A=sin^2A)now just divide both the terms by sin^2Awe get (1/sinA)-(cosA/sinA)which we can write as cosecA-cotA

in these type of question first observe what we have and what we needwe are given with sin and cos terms and we need answer in cosec and cot term so we will first multiply and divide by 1-cosAwe get sinA*(1-cosA)/(1+cosA)*(1-cosA)now open all the brackets and we getsinA-sinA.cosA/1-cos^2Awe can further simplify it assinA-sinAcosA/sin^2Ausing identity(1-cos^2A=sin^2A)now just divide both the terms by sin^2Awe get (1/sinA)-(cosA/sinA)which we can write as cosecA-cotAand that’s the answer

in these type of question first observe what we have and what we needwe are given with sin and cos terms and we need answer in cosec and cot term so we will first multiply and divide by 1-cosAwe get sinA*(1-cosA)/(1+cosA)*(1-cosA)now open all the brackets and we getsinA-sinA.cosA/1-cos^2Awe can further simplify it assinA-sinAcosA/sin^2Ausing identity(1-cos^2A=sin^2A)now just divide both the terms by sin^2Awe get (1/sinA)-(cosA/sinA)which we can write as cosecA-cotAand that’s the answer**if you like the solution please upvote**

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