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The value of tan-1\(\left(\cfrac{cos(\frac{15π}{4})-1}{sin(\frac{\pi}4)}\right)\) is equal to 

(A) -π/4 

(B) -π/8 

(C) -5π/12 

(D) -4π/9

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Best answer

 Correct option is (B) -π/8

\(tan^{-1}[\cfrac{cos(4π-π/4)-1}{sinπ/4}]\)

⇒ tan-1\((\frac{cos π/4 - 1}{sin π/4})\) 

tan-1(\(\frac{1-√2}1\)) = \(-\frac{\pi}8\)

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