Question

if sin theta - cos theta=0 find the value of sin 4 theta + cos4 theta

Answer 1

Given that,

sinA - cosA = 0

⇒ sinA = cosA

⇒ sinA/cosA = 1

⇒ tanA = 1

⇒ tanA = tan45°

⇒ A = 45°

∴ sin⁴A + cos⁴A

= sin⁴45° + cos⁴45°

= (1/√2)⁴ + (1/√2)⁴

= 1/4 + 1/4

= 2/4

= 1/2

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Answer 2

Step-by-step explanation:

given:sin theta - cos theta =0

let,theta be A

now ;sin A- cos A=0

sin A = cos A

sin A/cos A =1

=tan A =1

tan A = tan 45°

A=45°

sin^4+cos^4 A

sin^4 45°+cos^4 45°

(1/√2)^4+(1/√2)^4

1/4+1/4

2/4 = 1/2

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