Question

if tan theta = 1/ root 3 , prove that 7 sin square theta + 3 cos square theta = 4.​

Answer 1

Answer:

i hope this helps you out.

Answer 2

Given:

tanƟ = 1/√3 .

To Prove :

7sin²Ɵ +3cos²Ɵ = 4 .

Concept Used:

We know that tan equals to perpendicular/base.

So,using this concept we will find the values of sinƟ and cosƟ.

Answer:

We have ,

=>tanƟ = 1/√3.

=> tanƟ = tan30°

$\large\green{\boxed{\red{\sf{\leadsto \tan30\degree = \dfrac{1}{\sqrt{3}}}}}}$

Elimination of tan both sides.

.°. Ɵ =30°.

______________________________________

Now,

→ 7sin²Ɵ +3cos²Ɵ = 4 .

LHS = 7sin²Ɵ +3cos²Ɵ .

= 7 sin²30° + 3cos²30°

= 7 ×(1/2)² + 3× (√3/2)².

= 7×1/4 +3 × 3/4 .

=7/4 +9/4.

=7+9/4.

=16/4 .

=4 .

RHS = 4 .

.°. RHS = LHS

Hence Proved.