##
If sin θ – cos θ = 0, then the value of (sin
^{
4
}
θ + cos
^{
4
}
θ) is

## (A) 1

## (B) 3/4

## (C) 1/2

## (D) 1/4

NCERT Exemplar - MCQ

Chapter 8 Class 10 Introduction to Trignometry

Serial order wise

Last updated at Oct. 20, 2021 by Teachoo

Question 16 If sin θ – cos θ = 0, then the value of (sin4 θ + cos4 θ) is (A) 1 (B) 3/4 (C) 1/2 (D) 1/4 Given sin θ – cos θ = 0 sin θ = cos θ This can only happen if θ = 45° Now, sin4 θ + cos4 θ = sin4 45° + cos4 45° = (1/√2)^4+(1/√2)^4 = 2 × (𝟏/√𝟐)^𝟒 = 2 × [(1/√2)^2 ]^2 = 2 × [1/2]^2 = 2 × 1/4 = 𝟏/𝟐 So, the correct answer is (C)