Question

If cosec θ + cot θ = p, then prove that cos θ = p^2-1/p^2+1

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Answer 1

Answer:

Cosec A+cot A=P

1/sina+Cosa+sina=P

1+Cosa=psinA

squaring both sides

(1+cosA)^2=P^2(sinA)^2

(1+cosA)^2=P^2(1-(cos)^2)

(1+cosA)^2=P^2(1-(cos))(1+cosA)

(1+cosA) =P^2(1-cosA)

cosA =(P^2-1)(P^2+1)

hence proved