If sinθ - cosθ = 0, then the value of (sin⁴ θ + cos⁴ θ) is
a. 1
b. 3/4
c. 1/2
d. 1/4

Solution:

Given, sinθ - cosθ = 0

We have to find the value of sin⁴ θ + cos⁴ θ

sinθ = cosθ

We know that sin A/cos A = tan A

sinθ/cosθ = tanθ

So, tanθ = 1

θ = tan⁻¹(1)

tan 45° = 1

So, θ = 45°

Now, sin⁴ θ = sin⁴ 45°

From the above table,

sin 45° = 1/√2

So, sin⁴ 45° = (1/√2)⁴ = 1/4

Now, cos⁴ θ = cos⁴ 45°

From the above table,

cos 45° = 1/√2

So, cos⁴ 45° = (1/√2)⁴ = 1/4

sin⁴ θ + cos⁴ θ = 1/4 + 1/4

= (1 + 1)/4

= 2/4

= 1/2

Therefore, sin⁴ θ + cos⁴ θ = 1/2.

✦ Try This: If cosθ = 0, then the value of (sin³ θ + cos³ θ) is

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8

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NCERT Exemplar Class 10 Maths Exercise 8.1 Problem 13

If sinθ - cosθ = 0, then the value of (sin⁴ θ + cos⁴ θ) is a. 1, b. 3/4, c. 1/2, d. 1/4

Summary:

The sine of an angle is the ratio of the opposite side and the hypotenuse and the cosine of an angle is the ratio of the adjacent side and the hypotenuse. If sinθ - cosθ = 0, then the value of (sin⁴ θ + cos⁴ θ) is 1/2.

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☛ Related Questions:

• sin (45° + θ) – cos (45° – θ) is equal to a. 2cosθ, b. 0, c. 2sinθ, d. 1
• A pole 6 m high casts a shadow 2√3 m long on the ground, then the Sun’s elevation is a. 90°, b. 30°, . . . .
• The value of sinθ + cosθ is always greater than 1. Write ‘True’ or ‘False’ and justify your answer