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Question

tan[12cos1(53)]=

A
352
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B
3+52
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C
235
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D
23+5
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Solution

The correct options are
A 352
D 23+5
tan[12cos1(53)]
Let 12cos153=θcos2θ=53
But cos2θ=1tan2θ1+tan2θ53=1tan2θ1+tan2θ
5+5tan2θ=33tan2θ
(5+3)tan2θ=35tan2θ=353+5
tan2θ=(35)24tanθ=352
On rationalising
tanθ=352×3+53+5=23+5

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