Q.
If f(θ)=1−sin2θ+cos2θ2cos2θ, then value of f11∘⋅f34∘ is _______.
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answer is 0.5.
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Detailed Solution
f(θ)=1−sin2θ+cos2θ2cos2θ=(cosθ−sinθ)2+cos2θ−sin2θ2(cosθ−sinθ)(cosθ+sinθ)=cosθcosθ+sinθ=11+tanθf11∘⋅f34∘=11+tan11∘×11+tan34∘ =11+tan11∘×11+tan45∘−11∘ =11+tan11∘×11+1−tan11∘1+tan11∘ =11+tan11∘×1+tan11∘2 =12
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