Question

1/X [sin²5° + sin²85°/ cos²5° + cos² 85°] - 3/4= 1, find the value of X

Answer 1

SOLUTION

SO, HERE WE NEED TO FIND THE VALUE OF x

Given,

We are going to use the following identities which will help us in solving the question.And if you like the answer please mark braineliest.

We take the LHS first and simplify it,

LHS

first of all let us change the values using the identity

sin(90- \theta)=cos\theta

cos(90-\theta)=sin\theta

Therefore,

sin²5=sin²(90-85)=cos²85

cos²5=cos²(90-85)=sin²85

By putting the values,

We get,

$\frac{1}{x} ( \cos ^{2} (85) + \sin^{2} (85) )( \sin ^{2} (85) + \cos ^{2}(85)) - \frac{3}{4}$

Now, we will use the identity,

sin²\theta + cos²\theta=1

By putting the values we get,

$\frac{1}{ x } (1)(1) - \frac{3}{4} \\ = \frac{4 - 3x}{4x}$

Now LHS=RHS

WE HAVE,

$= > \frac{4 - 3x}{4x} = 1 \\ = > 4 - 3x = 4x \\ = > 4 = 7x \\ = > x = \frac{4}{7}$

So required value of x is 4/7

Answer 2

The value of x is 4/7