Question

cos^2 34° + cos2 56°
sin^2 59° + sin? 31°​

Answer 1

Question:

Evaluate:

$\displaystyle{\sf\:\dfrac{\cos^2\:34^{\circ}\:+\:\cos^2\:56^{\circ}}{\sin^2\:59^{\circ}\:+\:\sin^2\:31^{\circ}}}$

Answer:

$\displaystyle{\boxed{\red{\sf\:\dfrac{\cos^2\:34^{\circ}\:+\:\cos^2\:56^{\circ}}{\sin^2\:59^{\circ}\:+\:\sin^2\:31^{\circ}}\:=\:1}}}$

Step-by-step-explanation:

We have given that,

$\displaystyle{\sf\:\dfrac{\cos^2\:34^{\circ}\:+\:\cos^2\:56^{\circ}}{\sin^2\:59^{\circ}\:+\:\sin^2\:31^{\circ}}}$

We have to find the value of the given fraction.

Now,

$\displaystyle{\sf\:\dfrac{\cos^2\:34^{\circ}\:+\:\cos^2\:56^{\circ}}{\sin^2\:59^{\circ}\:+\:\sin^2\:31^{\circ}}}$

$\displaystyle{\implies\sf\:\dfrac{\cos^2\:34^{\circ}\:+\:\sin^2\:(\:90\:-\:56\:)^{\circ}}{\sin^2\:59^{\circ}\:+\:\sin^2\:31^{\circ}}\:\:\:-\:-\:-\:[\:\because\:\cos\:\theta\:=\:\sin\:(\:90\:-\:\theta\:)\:]}$

$\displaystyle{\implies\sf\:\dfrac{\cos^2\:34^{\circ}\:+\:\sin^2\:34^{\circ}}{\sin^2\:59^{\circ}\:+\:\cos^2\:(\:90\:-\:31\:)^{\circ}}\:\:\:-\:-\:-\:[\:\because\:\sin\:\theta\:=\:\cos\:(\:90\:-\:\theta\:)\:]}$

$\displaystyle{\implies\sf\:\dfrac{\cos^2\:34^{\circ}\:+\:\sin^2\:34^{\circ}}{\sin^2\:59^{\circ}\:+\:\cos^2\:59^{\circ}}}$

$\displaystyle{\implies\sf\:\dfrac{1}{1}\:\:\:-\:-\:-\:[\:\because\:\sin^2\:\theta\:+\:\cos^2\:\theta\:=\:1\:]}$

$\displaystyle{\implies\sf\:1}$

$\displaystyle{\therefore\:\underline{\boxed{\red{\sf\:\dfrac{\cos^2\:34^{\circ}\:+\:\cos^2\:56^{\circ}}{\sin^2\:59^{\circ}\:+\:\sin^2\:31^{\circ}}\:=\:1}}}}$

Answer 2

brainliest answer bro