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Answer:
SORRY
Step-by-step explanation:
It is too hard .....
Answered by
0
Step-by-step explanation:
This is easy my dear. Here's a proof.
SinA/(1 + CosA) + (1 + CosA)/SinA
= [(SinA)^2 + (1+CosA)^2]/[SinA(1 + CosA)]
= [(SinA)^2 + (CosA)^2 + 1 + 2CosA]/[SinA(1 + CosA)]
= [2(1 + CosA)]/[SinA(1 + CosA)] ( since, (SinA)^2 + (CosA)^2 = 1 )
= 2/SinA = 2CosecA, Hence LHS=RHS.
2. To prove the identity : [(1-cos A)/(1+cos A)]^0.5 = cosec A - cot A.
LHS = [(1-cos A)/(1+cos A)]^0.5
= [(1-cos^2 A/2+sin ^2 A/2)/(1+cos^2 A/2 - sin^2 A/2)]^0.5
= [(2 sin^2 A/2)/2 cos^2 A/2)]^0.5
= [tan^2 A/2]^0.5 = tan A/2 …(1)
RHS = cosec A - cot A
= (1/sin A)-(cos A/sin A)
= (1-cos A)/sin A
= (1-cos^2 A/2+sin^2 A/2)/2 sin A/2 cos A/2
= 2 sin^2 A/2/2 sin A/2 cos A/2
= (sin A/2)/(cos A/2)
= tan A/2 …(2)
Since (1) and (2) are the same the identity is proved.
Hope you understand.
Best wishes.
pls mark a s brainliest
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