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Question

Mathematics Question on Differential equations

The value of tan−1(cos154−1sin(π4)) tan^{-1}(\frac{cos\frac{15}{4}-1}{sin(\frac{π}{4})} ) is equal to:

A

−π4-\frac{\pi}{4}

B

−π8-\frac{\pi}{8}

C

−5π12-\frac{5\pi}{12}

D

−4π9-\frac{4\pi}{9}

Answer

−π4-\frac{\pi}{4}

Explanation

Solution

The correct option is(B): −π8-\frac{\pi}{8}

tan−1(cos154−1sin(π4))tan^{-1}(\frac{cos\frac{15}{4}-1}{sin(\frac{π}{4})} )

=tan−1(12−112)=tan^{-1}(\frac{\frac{1}{\sqrt2}-1}{\frac{1}{\sqrt2}})

=tan−1(1−2)=−tan−1(2−1)=tan^{-1}(1-\sqrt2)=-tan^{-1}(\sqrt2-1)

=−π8=-\frac{\pi}{8}