If 5 sin2 θ + cos2 θ = 2, find the value of sin θ.

Given: 5 sin2 θ + cos2 θ = 2⇒ 5 sin2 θ + (1– sin2 θ) = 2 [∵ sin2 θ + cos2 θ = 1]⇒ 5 sin2 θ + 1 – sin2 θ = 2⇒ 4 sin2 θ = 2 – 1⇒ 4 sin2 θ = 1

Q48 of 268 Page 4

If 5 sin² θ + cos² θ = 2, find the value of sin θ.

Given: 5 sin² θ + cos² θ = 2

⇒ 5 sin² θ + (1– sin² θ) = 2 [∵ sin² θ + cos² θ = 1]

⇒ 5 sin² θ + 1 – sin² θ = 2

⇒ 4 sin² θ = 2 – 1

⇒ 4 sin² θ = 1

In the given figure, find 3 tan θ – 2 sin α + 4 cos α.

In the given figure ABC is right angled at B and BD is perpendicular to AC. Find (i) cos θ, (ii) cot α.

If 7 sin² θ + 3 cos² θ =4, find the value of tan θ.

If 4 cos θ + 3 sin θ = 5, find the value of tan θ.