Question

If tan 2 45° − cos 2 60 ° = x sin 2 45 ° tan 2 60 °, then 'x' is equal to .........

Answer 1

Hey.......!!! here is ur answer.....☺️☺️☺️

Given that.....

tan²45 – cos²60 = x sin²45 tan²60

=>(1)² – (1/2)² = x(1/√2)²(√3)²

{ we know that tan45 = 1, cos60 = 1/2 ,
sin45 = 1/√2 , tan60 = √3}

=>1–1/4 = 3x/2

=>3/4 = 3x/2

=>x = 2/4

=>x = 1/2 <<<Ans.

I hope it will help you.......✌️✌️✌️

Answer 2

Given:

A trigonometric equation$tan^2(45)- cos^2(60) = x * sin^2(45) * tan^2 (60)$,

To Find:

The value of x from the given expression.

Solution:

The given problem can be solved using the concepts of trigonometric ratios.

1. The given trigonometric equation is tan²45° - cos²60° = x * sin²45° * tan²60°.

2. The values of tan 45°, cos60°, sin45°, tan60° is 1, (1/2), (1/√2), √3 respectively.

3. Substitute the above values in the given equation,

=> (1)² - (1/2)² = x * (1/√2)² * (√3 )²,

=> 1 - (1/4) = x * (1/2) * 3,

=> (3/4) = x * 3/2,

=> (3/4) = (3x/2),

=> x = (2/4),

=> x = 1/2=0.5.

4. x=0.5 satisfies the equality.

Therefore, the value of x in the given equation is 0.5 (OR) 1/2.