Question

If 7sin^2 theta+3cos2theta=4 then the value of tan^2theta

Answer 1

HEYA !!!

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As,

$7sin^2Φ$ + $3cos^2Φ$ = 4

Then,

$7sin^2Φ$ = $3sin^2Φ$$4sin^2Φ$

Now,

$3sin^2Φ$ + $4sin^2Φ$ + $3cos^2Φ$ = 4

As, $Sin^2Φ$ + $Cos^2Φ$ = 1

So,

$4sin^2Φ$ + 3(1) = 4

$4sin^2Φ$ = 4 - 3

$sin^2Φ$ = $\frac{1}{4}$

SinΦ = 1/√4

...

Now,

$Tan^2Φ$ = $sin^2Φ$ / $cos^2Φ$

So,

$Tan^2Φ$ = (1/4) / (1-$sin^2Φ$)

$Tan^2Φ$ = (1/4) / (1-1/4)

$Tan^2Φ$ = (1/4) / (3/4)

$Tan^2Φ$ = $\frac{4}{12}$

$Tan^2Φ$ = $\frac{1}{3}$

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THANKS..

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 .