Question

If tan theta + cot theta =4 ,then find tan ^4 theta + cot ^4 theta​

Answer 1

Answer:

it is given that:

tan theta +cot theta=4..............(1)

than:

tan^4 theta + cot^4 theta

we can write

(tan theta + cot theta)^4

by equation (1)

=(4)^4

=256

Answer 2

Given:-

• tanθ + cotθ = 4

To Find:-

• The value of tan⁴θ + cot⁴θ

Solution:-

As we are given:- tanθ + cotθ = 4

Let us square both LHS and RHS

= (tanθ + cotθ)² = (4)²

= tan²θ + cot²θ + 2tanθcotθ = 16

= tan²θ + cot²θ + 2 × tanθ × 1/tanθ = 16

= tan²θ + cot²θ + 2 = 16

= tan²θ + cot²θ = 16 - 2

= tan²θ + cot²θ = 14

So we got the value of tan²θ + cot²θ as 14

Now we'll square these again,

Hence,

(tan²θ + cot²θ)² = (14)²

= tan⁴θ + cot⁴θ + 2tan²θcot²θ = 196

= tan⁴θ + cot⁴θ + 2 × tan²θ × 1/tan²θ = 196

= tan⁴θ + cot⁴θ + 2 = 196

= tan⁴θ + cot⁴θ = 196 - 2

= tan⁴θ + cot⁴θ = 194

Therefore the value of tan⁴θ + cot⁴θ is 194.

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Important:-

These points must be kept in mind while solving such questions.

• Sinθ = 1/Cosecθ
• Cosecθ = 1/Sinθ
• Cosθ = 1/Secθ
• Secθ = 1/Cosθ
• Tanθ = 1/Cotθ
• Cotθ = 1/Tanθ

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