Question

if 7sin^2 theta + cos^2 theta = 44. Show that tan theta = 1 by √3

Answer 1

plz check the question once again

Answer 2

Answer:

Given:

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

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

Consider,

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

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

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

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

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

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

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

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

Using trigonometric ratio,

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

Figure is attached,

CB² = AC² - AB²  ( Pythagoras theorem )

CB² = 2² - 1²

CB² = 4 - 1

CB² = 3

CB = √3

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

Hence Proved.