Question

9. If 7 sin2

θ+ cos2

θ=44, show that tan=1/√3

Answer 1

Answer:

Given:

$7sin^2\,\theta+3cos^2\,\theta=4$

To show: $tan\,\theta=\frac{1}{\sqrt{3}}$

Consider,

$7sin^2\,\theta+3cos^2\,\theta=4$

$4sin^2\,\theta+3sin^2\,\theta+3cos^2\,\theta=4$

$4sin^2\,\theta+3(sin^2\,\theta+cos^2\,\theta)=4$

$4sin^2\,\theta+3(1)=4$

$4sin^2\,\theta=4-3$

$sin^2\,\theta=\frac{1}{4}$

$sin\,\theta=\sqrt{\frac{1}{4}}$

$sin\,\theta=\frac{1}{2}$

We know that,

$sin\,\theta=\frac{Opposite}{Hypotenuse}=\frac{1}{2}$

from attached figure

XZ² = XY² - YZ²  ( Pythagoras theorem )

XZ² = 2² - 1²

XZ² = 4 - 1

XZ² = 3

XZ = √3

⇒ $tan\,\theta=\frac{Opposite}{Adjacent}=\frac{1}{\sqrt{3}}$

Hence Proved.

Answer 2

Answer:

The correct question is  :   7Sin^2A+ 3cos^2A = 4  , prove tan = 1/root3

Step-by-step explanation:

Given that:

7 Sin^2A + 3 cos^2A = 4

On dividing by cos^2A both sides

7Tan^2A + 3 = 4/Cos^A

7Tan^2A + 3 = 4 Sec^A

7Tan^2A + 3 = 4(1+Tan^A)

7Tan^2A + 3 = 4 + 4Tan^A

3Tant^A = 1

Tan^A = 1/3

TanA = 1/Root3

Hence Proved  

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