General Aptitude TestQuantitative ReasoningTrigonometry

If sin θ - cos θ = 0, 0^° < θ < 90^°, then the value of sin^4 θ + cos…

If $\sin \theta - \cos \theta = 0, 0^\circ < \theta < 90^\circ$, then the value of $\sin^4 \theta + \cos^4 \theta$ is:

Answer & explanation

Correct answer: option 3

Provided:-

sinθ - cosθ = 0

sinθ = cosθ

{ we know that if sinA = cosB then A + B = 90º }

So, θ + θ = 90º

θ = 45º

Now,

sin4θ + cos⁴θ

= sin445º + cos⁴45º

= ($\frac{1}{√2}$)4 + ($\frac{1}{√2}$)4

= $\frac{1}{2}$