Domain and Range of Basic Inverse Trigonometric Functions
Is LHS=RHS? ...
Question
Is LHS=RHS? (1+1tan2θ)(1+1cot2θ)=1sin2θ−sin4θ Say yes or no.
A
Yes
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B
No
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C
Ambiguous
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D
Data insufficient
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Solution
The correct option is B Yes LHS=(1+1tan2θ)(1+1cot2θ) =(tan2θ+1tan2θ)(cot2θ+1cot2θ)=(sec2θ)(cosec2θ)(tanθcotθ)2 =sec2θcosec2θ1=1cos2θ×1sin2θ=1(1−sin2θ)sin2θ=1sin2θ−sin4θ=RHS