Question

( sinA + cosecA )² + ( cosA + secA )² = 7 + tan²A + cot²A​

Answer 1

Step-by-step explanation:

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Answer 2

Solution:

We know that sin2θ+cos2θ=1

i.e. 1-cos2θ=sin2θ

∴(1-cosθ)(1+cosθ)=sinθ.sinθ

∴

1-cosθ

sinθ

=

sinθ

1+cosθ

, OR

sinθ

1+cosθ

=

1-cosθ

sinθ

(by theorem on equal ratios)

=

(1-cosθ)-(sinθ)

(sinθ)-(1-cosθ)

∴

sinθ

1+cosθ

=

1-cosθ-sinθ

sinθ-1-cosθ