Question

Sin^2 (2x-10)+sin^2 30°=1
solve for x

Answer 1

Step-by-step explanation:

Sin^2 (2x-10)+sin^2 30°=1

Sin^2 (2x-10)+1/2^2=1

Sin^2(2x-10)=1-1/4

Sin^2(2x-10)=3/4-------(I)

We know that

sin60 = √3/2

or,sin^2 (60)=3/4-------(II)

From (I) and (II) we obtain:

Sin^2(2x-10)=sin^2 (60)

2x-10=60

or, 2x=70

or, x=35

Answer 2

Question:-

sin²(2x-10) + sin²30° = 1

Solve for x

Solution:-

We have,

$\sin30° = \frac{1}{2}$

Then

$\sin ^{2} 30° = ( { \frac{1}{2}) }^{2}$$= \frac{1}{4}$

So,

${ \sin }^{2} (2x - 10) + \frac{1}{4} = 1$

${ \sin }^{2} (2x - 10) = 1 - \frac{1}{4}$ $= \frac{3}{4}$

We have ,

$\sin60° = \frac{ \sqrt{3} }{2}$

So,

${ \sin }^{2} 60° = \frac{3}{4}$

Therefore,

${ \sin }^{2} (2x - 10) = { \sin }^{2} 60°$

It becomes

$2x - 10 = 60°$

$2x = 60 °+ 10°$

$2x = 70$

$x = \frac{70}{2}°$

$x = 35°$