Question

if 7sin^2 theta+3cos^2theta=4 find tan theta

Answer 1

According to question

7 Sin^2 theta + 3 Cos^2 theta = 4
Separating

3 Sin^2 theta + 3 Cos^2 theta + 4 Sin^2 theta = 4
3 (Sin^2 theta + Cos^ theta) + 4 Sin^2 theta = 4
We know
Sin^2x+Cos^2x = 1
Thus 
3*1 + 4 Sin^2 theta =4
        4 Sin^2 theta =1
           Sin^2 theta = 1/4
              Sin theta = 1/2

Putting Sin theta in above equaton

        7 *1/4 + 3 Cos^2 theta =4
                      3 Cos^2 theta = 9/4
                         Cos^2 theta = 3/4
                            Cos theta = root 3/2

Thus
                   tan theta = Sin theta/Cos theta
                                  = 1/2  /   root3 / 2
                                  = 1/root3
Thus 
tan theta = 1/root3

Answer 2

Step-by-step explanation:

Answer :-

→ tan30° = 1/√3

Step-by-step explanation :-

We have,

→ 7 sin² ∅ + 3 cos² ∅ = 4 .

⇒ 4 sin²∅ + 3 sin²∅ + 3 cos²∅ = 4 .

⇒ 4 sin²∅ + 3( sin²∅ + cos²∅ ) = 4 .

⇒ 4 sin²∅ + 3( 1 ) = 4 . [ ∵ sin²∅ + cos²∅ = 1 ] .

⇒ 4 sin²∅ + 3 = 4 .

⇒ 4 sin²∅ = 4 - 3 .

⇒ 4 sin²∅ = 1 .

⇒ sin²∅ = 1/4 .

⇒ sin ∅ = √(1/4) .

∴ sin ∅ = 1/2 .

But, sin 30° = 1/2 .

Then, sin ∅ = sin 30° .

$\huge \pink{ \boxed{ \it \therefore \theta = 30 \degree.}}$

Then, tan 30° = 1/√3 .

Hence, it is proved .