Prove the following: cos θ sin (90° – θ) + sin θ cos (90° – θ) = 1

Prove the following:

……………………

Answer :

= cos θ/cos θ + sin θ/sin θ

= 1 + 1

= 2

= RHS

(ii) cos θ sin (90° – θ) + sin θ cos (90° – θ) = 1

LHS = cos θ sin (90° – θ) + sin θ cos (90° – θ)

= cos θ. cos θ + sin θ. sin θ

= cos² θ + sin² θ

= 1

= RHS

= tan θ/cot θ + cos θ/cos θ

= (tan θ × tan θ) + 1

= tan² θ + 1

= sec² θ

= RHS

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