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A day full of math games & activities. Find one near you.
If 2sin2 θ - cos2 θ = 2, then find the value of θ
Solution:
It is given that
2 sin2 θ - cos2 θ = 2
As sin2 θ + cos2 θ = 1
We get cos2 θ = 1 - sin2 θ
2 sin2 θ - (1 - sin2 θ) = 2
By further simplification
2 sin2 θ - 1 + sin2 θ = 2
3 sin2 θ = 3
Divide both sides by 3
sin2 θ = 1
Taking square root on both sides
sin θ = 1
So we get
θ = sin-1 (1)
θ = 90°
Therefore, the value of θ is 90°.
✦ Try This: Show that tan4 θ +tan2 θ = sec4 θ -sec2 θ.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.3 Problem 12
If 2sin2 θ - cos2 θ = 2, then find the value of θ
Summary:
The sine of an angle of a right-angled triangle is the ratio of its perpendicular (that is opposite to the angle) to the hypotenuse. If 2sin2 θ - cos2 θ = 2, the value of θ is 90°
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