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Question

If tan2θ=1e2, then the value of secθ+tan3θcscθ is ?

A
(2e2)32
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B
(2e2)12
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C
(2+e2)12
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D
(2+e2)32
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Solution

The correct option is B (2e2)32
tan2θ=1e2

e2=1tan2θ

Also sec2θ=2e2

The above expression can be expressed in terms of powers of secθ

secθ+tan3θcscθ=(2(1tan2θ))n

1cosθ+sin3θcos3θ×1sinθ=(1+tan2θ)n

1cos3θ=(sec2θ)n

3=2n

n=32

secθ+tan3θcscθ=(2(1tan2θ))32

secθ+tan3θcscθ=(2e2)32


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