Question

If 0°<θ<90°
2sin²θ + 3cosθ = 3, then the value of θ is ???

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Answer 1

Answer:

Required measure of angle A is 90°.

Step-by-step explanation:

= > cos^2 A - 3 cosA + 2 = 2 sin^2 A

From the properties of trigonometry :

sin^2 theta + cos^2 theta= 1

sin^2 theta= 1 - cos^2 theta

theta will be cancelled

= > cos^2 A - 3 cosA + 2 = 2( 1 - cos^2 A ) { 2sin^2 A = 2( 1 - cos^2 A ) }

= > cos^2 A - 3 cosA + 2 = 2 - 2 cos^2 A

= > 2 cos^2 A + cos^2 A - 3 cosA + 2 - 2 = 0

= > 3 cos^2 A - 3 cosA = 0

= > 3 cosA ( cosA - 1 ) = 0

Case 1 : If cosA is 0 .

= > 3 cosA = 0

= > cosA = 0

= > cosA = cos90°

= > A = 90° or π / 2

Case 2 : If cosA - 1 is zero.

= > cosA - 1 = 0

= > cosA = 1

= > cosA = cos0°

But here, theta or A is greater than 0°, cosA ≠ cos0°

Therefore the required measure of angle A is 90°.

This is your answer

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