Question

If tan theta + cot theta = 1 , write the value of tan4 theta + cot4 theta.

Answer 1

Hey !!!

tan¢ + cot¢ = 1 (given )

Squaring on both side .

(tan¢ + cot¢ )² = 1²

tan²¢ + cot²¢ + 2tan¢ × cot¢ = 1

tan²¢ + cot²¢ + 2 = 1

tan²¢ + cot²¢ = - 1___________1)

Now , from given .

tan⁴¢ + cot⁴¢ = ?

As we know that . ..

a⁴ + b⁴ = (a²)² + (b²)² = (a² + b² ) ² - 2ab

similarly ,

tan⁴¢ + cot⁴¢ = (tan²¢ + cot²¢ )² - 2tan¢ × cot¢

(-1)² - 2× 1 [from 1st ]

hence, tan⁴¢ + cot⁴¢ = - 1 Answer ✔

____________________________

Hope it helps you !!!

@Rajukumar111

Answer 2

Step-by-step explanation:

hope its helpful

I hope its the correct answer