Question

sin⁴ theta-cos⁴theta=



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Answer 1

Answer:

(sin Θ + cos Θ)(sin Θ - cos Θ)

Step-by-step explanation:

sin⁴Θ - cos⁴Θ

= (sin²Θ)² - (cos²Θ)²  - using a² - b² = (a+b)(a-b)

= (sin²Θ + cos²Θ)(sin²Θ - cos²Θ) - using a² - b² = (a+b)(a-b)

= (1)(sin Θ + cos Θ)(sin Θ - cos Θ) -----  sin²Θ + cos²Θ = 1

= (sin Θ + cos Θ)(sin Θ - cos Θ)

Answer 2

*Question:—

→ sin⁴ theta-cos⁴theta = ?

*Answer:—

→ sin⁴ theta - cos⁴theta = 1 - 2cos² theta.

If you have to prove it then :—

LHS = ( sin⁴∅ -cos⁴∅)

=( sin²∅ -cos²∅)(cos²∅ +sin²∅)

we know ,

sin²∅ + cos²∅ = 1

= (sin²∅ -cos²∅).1 = RHS

Hence,

LHS = RHS. proved.

$@ vikramjeeth$