Question

7 Sin² theta + 3 Cos² theta = 4

find the value of Sec² theta

$7\sin^{2}\theta\:+\:3\cos^{2} \theta\:=\:4 \\ \\ \\ \sec\theta\: =$







​

Answer 1

Answer:

7sin

2

θ+3cos

2

θ=4

⇒7sin

2

θ+3(1−sin

2

θ)=4

⇒7sin

2

θ+3−3sin

2

θ=4

⇒4sin

2

θ=1

⇒sin

2

θ=

4

1

⇒sinθ=

2

1

⇒sinθ=sin30

∘

⇒θ=30

∘

L.H.S =secθ+cosecθ

=sec30

∘

+cosec30

∘

=

3

2

+2

= R.H.S

Hence proved.