If sec theta cos theta sin theta radic 2 then the value of 2sin theta cos theta minus sin theta is e...........

Quantitative Aptitude ( CCS) Trignometry

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If secθ(cosθ+sinθ)=√2 then the value of 2sinθcosθ−sinθ is equal to,

√2

3√2

3/√2

1/√2

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Explanation:

From the given equation it is easy to evaluate the value of tanθ,
secθ(cosθ+sinθ)=√2,
Or, 1+tanθ=√2
Or, tanθ=√2−1.
As the target expression is in sin and cos we can easily convert the expression wholly in terms of tanθ and then substitute the value of tanθ,
2sinθ/(cosθ−sinθ)
=2tanθ/(1−tanθ), dividing both numerator and denominator by cosθ,
=2(√2−1)/(2−√2)
=2(√2−1)/√2(√2−1)
=√2