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Find the value of sin(80° + θ) + cos(65° + θ) - cos(10° - θ) + tan2θ - cosec2(90° - θ) - sin(25° - θ)

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Correct Answer - Option 3 : -1

Formula used :

sin(90° - θ) = cosθ 

cos(90° - θ) = sinθ 

cosec(90° - θ) = secθ 

tan2θ - sec2θ = -1  

Calculations :

sin(80° + θ) + cos(65° + θ) - cos(10° - θ) + tan2θ - cosec2(90° - θ) - sin(25° - θ)

⇒ sin(80° + θ) - cos(10° - θ) + cos(65° + θ) - sin(25° - θ) + tan2θ - cosec2(90° - θ)

⇒ sin(80° + θ) - sin(90° - (10° - θ) + cos(65° + θ) - cos(90° - (25° - θ) + tan2θ - cosec2(90° - θ).

⇒ sin(80° + θ) - sin(80° + θ) + cos(65° + θ) - cos(65° + θ) + tan2θ - sec2θ

⇒ 0 + 0 + (-1) 

⇒ -1 

∴ Option 3 is the correct choice 

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