Question

Evaluate $\displaystyle{\sf{cosec^2 \frac{\pi }{16}-tan^2\frac{7\pi }{16}. }}$

Answer 1

$\displaystyle{\sf{cosec^2\frac{\pi }{16}-tan^2\frac{7\pi }{16} }}\\\\\\\displaystyle{\sf{=cosec^2\frac{\pi }{16}-cot^2\frac{\pi }{16} }}\\\\\\\underline{\boxed{\displaystyle{\sf{=1}}}}$

$\displaystyle{\textsf{We know that, tan}\sf{\frac{7\pi }{16} =cot\frac{\pi }{16},\ because\ they\ are\ \bold{complementary\ angles.} }}$

$\displaystyle{\sf{\frac{\pi }{16}+\frac{7\pi }{16}=\frac{8\pi }{16} =\frac{\pi }{2}\ which\ when\ converted\ to\ degrees\ becomes\ 90 \°. }}$

Calculation :-

$\displaystyle{\sf{Radian=\frac{\pi Degree}{180} }}\\\\\displaystyle{\sf{\implies D=\frac{180R}{\pi } }}\\\\\displaystyle{\sf{\implies D=\frac{180*\frac{\pi }{2} }{\pi } }}\\\\\displaystyle{\sf{\implies D=\frac{90\pi }{\pi } }}\\\\\displaystyle{\sf{\implies \boxed{D=90\°}}}$

Answer 2

my hand writting is not good but answer is s correct follow me ok ok

$\mathcal{thanks\: bro} [/t$Input:[Tex]\boxed{Box}[/Tex

:$\red{Cloud}$

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