Question

Evaluate
(sin^2 20*+sin^2 70*/cos^2 20*+cos^2 70* )+(sin (90*-0)sin 0/tan 0) + cos (90*-0)cos 0/cot 0=?
(0-theta )

Answer 1

$\textbf{\large{\underline{\underline{\pink{Step by step Explanation:-}}}}}$

$\mathtt{( \frac{\sin^2(20°)+\sin^2(70°)}{\cos^2(20°)+\cos^2(70°)} )+(\sin(90°-\Theta))\frac{\sin{\Theta}}{\tan{\Theta}}+(\cos(90°-\Theta)\frac{\cos{\Theta}}{\cot{\Theta}}})$

$\mathtt{=( \frac{\sin^2(20°)+\cos^2(90°-70°)}{\sin^2(90°-20°)+\cos^2(70°)} )+(\cos{\Theta})(\frac{\sin{\Theta}}{\frac{\sin{\Theta}}{\cos{Theta}}})+(\sin{\Theta}\frac{\cos{\Theta}}{\frac{\cos{\Theta}}{\sin{\Theta}}}}$

$\mathtt{=( \frac{\sin^2(20°)+\cos^2(20°)}{\sin^2(70°)+\cos^2(70°)} )+(\cos{\Theta}\frac{\sin{\Theta}}{\sin{\Theta}}\times{\cos{\Theta}}+(\sin{\Theta})\frac{\cos{\Theta}}{\cos{\Theta}}\times{\sin{\Theta}}}$

$\mathtt{=1+\cos^2{\theta}+\sin^2{\theta}}$

$\mathtt{=1+1}$

$\mathtt{=2}$

$\mathtt{\boxed{\green{By,D.pradhan}}}$

Hope it'll be helpful to you..