If θ < 90°, find the value of: sin2θ + cos2θ

If θ < 90°, find the value of: sin²θ + cos²θ

Sum

Since θ <90°,
Consider θ = 45°
∴ sin² + cos²
= sin²45° + cos²45°

= `(1/sqrt(2))^2 + (1/sqrt(2))^2`

= `(1)/(2) + (1)/(2)`
= 1.

shaalaa.com

Trigonometric Equation Problem and Solution

Is there an error in this question or solution?

Chapter 27: Trigonometrical Ratios of Standard Angles - Exercise 27.1

Chapter 27 Trigonometrical Ratios of Standard Angles
Exercise 27.1 | Q 19.1

If 4 sin² θ – 1 = 0 and angle θ is less than 90°, find the value of θ and hence the value of cos² θ + tan² θ.

If 4 cos² x = 3 and x is an acute angle;
find the value of :
(i) x
(ii) cos² x + cot² x
(iii) cos 3x (iv) sin 2x

Solve the following equation for A, if sec 2A = 2

If sin α + cosβ = 1 and α= 90°, find the value of 'β'.

If θ = 30°, verify that: tan2θ = `(2tanθ)/(1 - tan^2θ)`

Find the value of 'y' if `sqrt(3)` = 1.723.
Given your answer correct to 2 decimal places.

Evaluate the following: `(sin25° cos43°)/(sin47° cos 65°)`

Evaluate the following: sin22° cos44° - sin46° cos68°

Evaluate the following: sin(35° + θ) - cos(55° - θ) - tan(42° + θ) + cot(48° - θ)

Prove the following: tanθ tan(90° - θ) = cotθ cot(90° - θ)