Question

If sin theta - cos theta = 0, then the value of sin4 theta + cos4 theta is:
(a) 1
(b) _3
(c) _1
(d) 1​

Answer 1

Answer:

given that

sinø-cosø=0

sinø= cosø

ø = 45°

sin4ø + cos 4ø

= sin180° + cos 180°

= 0 + (-1)

= -1

Answer 2

The required "option c) - 1" is correct.

Step-by-step explanation:

We have,

$\sin \theta-\cos \theta$ = 0

To find, the value of $\sin^4 \theta+\cos^4 \theta$ = ?

∴ $\sin^4 \theta+\cos^4 \theta$

= $(\sin^2 \theta)^2+(\cos^2 \theta)^2$

Using the algebraic identity,

$(a+b)^{2}=a^{2}+b^{2}+2ab$

⇒ $a^{2}+b^{2}=(a+b)^{2}-2ab$

= $(\sin^2 \theta+\cos^2 \theta)^2-2\sin^2 \theta.\cos^2 \theta$

Using the trigonometric identity,

$\sin^2 \theta+\cos^2 \theta$ = 1

= 1 - 2 = - 1

Thus, the required "option c) - 1" is correct.