Question

I want the answer .............................​

Answer 1

Answer:

L.H.S

=(1+ cos A /sinA + sinA/cosA)(sinA-CosA

=(cosAsinA + cos^2A + Sin^2A/cosAsinA )(sinA- cosA). .....(take LCM)

=(cosA sinA + 1/cosAsinA) (sin A- cos A ). .....(sin^2A +cos^2 A = 1)

= cosA sin^2A -cos^2 A sin A + sinA - cosA / cos A sin A

=sinA ( 1 - cos^2 A) -cosA (1- sin^2A)/ cosAsinA

sinA sin^2A - cos A cos^2 /cosAsinA

sin^3A - cos^3A/cosAsinA

sin^3A/ sinAcosA - cos^3A/cosA sinA

sin^2A /cosA - cos^2 /SinA

=secA/ cosecA - cosecA / sec^2. HENCE PROVED

L.H.S = R.H.S

Step-by-step explanation:

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Answer 2

step by step explaination

taking LHS

SinATanA-CotACosA=SinA×SinA/CosA -cosA×CosA/Sin A

=Sin^2A/Cos A -Cos^2A/SinA

taking LCm as sinAcos A we get

(sin^3A-cos^3A)×1/sinAcosA

(SinA-cosA) +(sin^2A +Cos^A + sinAcos A)×1/sinAcosA

(1/cosA-1/SinA)+(1/sinAcosA+1)

1/sinAcos^2A. -1/sin^AcosA +1/cosA

taking LCM as SinAcosA

we will get

(cosA-SinA+SinA)×1/sinAcosA

cosA/SinAcosA

1/SinA

sec A

similarly u can show the third part of this question.

U can do it easily by converting tanA into sin and cos terms

hope you understand it dude