Question

If cos 4 alfa =sin 2 alpha then value of tan 4alpha

Answer 1

value of tan4α = 1

it is given that, cos4α = sin2α then we have to find tan4α.

we know, cosθ = sin(90° - θ)

so, cos4α = sin(90° - 4α).......(1)

now cos4α = sin2α

from equation (1),

sin(90° - 4α) = sin2α

⇒90° - 4α = 2α

⇒90° = 2α + 6α

⇒α = 90°/8 = 11.5°

now value of tan4α = tan4(11.5°)

= tan45° = 1

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