Question

if alpha+beta=90 and alpha=2beta then cos2alpha+sin2beta is​

Answer 1

Solution :

Alpha and beta are two angles such that alpha + beta = 90 degrees .

It is obvious that alpha and beta are complementary angles .

alpha = 2 ( beta )

alpha + beta = 90

> 2 beta +beta = 90

> 3 beta = 90

> beta = 30

> alpha = 60

cos 2 alpha + sin 2 beta

> cos 120 + sin 60

>-1/2 + root 3/2

> ( root 3 - 1)/2

This is the required answer.

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Answer 2

Answer:

Required Answer :-

As we are knowing that

Alpha + Beta = 90

Now,

$\alpha = 2 \beta$

$2 \beta + \beta \: = 90$

$\sf \: 3 \beta = 90$

$\beta = 30$

Now,

$\sim \: \alpha = 90 - \beta$

$\alpha = 90 - 30$

$\alpha = 60$

$\cos 2 \: \alpha + \sin2 \beta$

$\cos(160) + \sin(60)$

$\dfrac{ - 1}{2} + \dfrac{ \sqrt{3} }{2}$

$\sf \: \dfrac{ \sqrt{3} - 1}{2}$