Question

if 7 sin²theta +3cos²theta=4, show that tan theta=√⅓

Answer 1

Hey !!!

7sin²¢ + 3cos²¢ = 4

{✔dividing by cos²¢ on both side }

= 7sin²¢ + 3cos²¢ /cos²¢ = 4/cos²¢

= 7tan²¢ + 3 = 4sec²¢

= 7tan²¢ + 3 = 4 ( 1 + tan²¢ )

{•°•sec²¢ = 1 + tan²¢ }

= 7tan²¢ + 3 = 4 +4tan²¢

= 3tan²¢ = 4 - 3

= tan²¢ = 1/3

=> tan¢ = +-√1/3 prooved

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Hope it helps you !!

@Rajukumar111

Answer 2

Hi there!

Given :-

7 sin²θ  + 3 cos²θ  = 4

Dividing both sides of the Eqn. by cos²θ :-

⇒ 7 tan²θ + 3 = 4 / cos²θ

⇒ 7 tan²θ + 3 = 4 sec²θ

⇒ 7 tan²θ + 3 = 4(1 + tan²θ)

⇒ 7 tan²θ + 3 = 4 + 4 tan²θ

⇒ 3 tan²θ = 1

⇒ tan²θ = 1 / 3

⇒ tanθ = ± √1 / 3

[ Hence Proved. ]

Hope it helps! :)