Question

if sintheta–costheta=0 then the value of sin⁴theta+cos⁴theta is​

Answer 1

Step-by-step explanation:

sin theta - cos theta =0

sintheta=costheta

therefore theta=45

sin⁴45+cos⁴45=

(1/√2)⁴+(1/√2)⁴=

1/4+1/4=1/2

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Answer 2

Step-by-step explanation:

Given :-

Sin θ - Cos θ = 0

To find :-

Fond the value of Sin⁴θ + Cos⁴θ ?

Solution :-

Method-1:-

Given that

Sin θ - Cos θ = 0

=>Sin θ = Cos θ

=> Sin θ = 1×Cos θ

=> Sin θ/Cos θ = 1

=> Tan θ = 1

=> Tan θ = Tan 45°

=> θ = 45°

Now,

Sin⁴θ + Cos⁴ θ

=> (Sin 45°)⁴ + (Cos 45°)⁴

=> (1/√2)⁴+(1/√2)⁴

=> (1/4)+(1/4)

=> (1+1)/4

=> 2/4

=> 1/2

Method -2:-

Given that

Sin θ - Cos θ = 0

=>Sin θ = Cos θ

=> Sin θ = 1×Cos θ

=> Sin θ/Cos θ = 1

=> Tan θ = 1

=> Tan θ = Tan 45°

=> θ = 45°

Now,

Sin⁴θ + Cos⁴ θ

We know that

Sin⁴θ+ Cos⁴θ = 1-2Sin² θ Cos²θ

=> 1-2(1/√2)²(1/√2)²

=> 1-2(1/2)(1/2)

=> 1-2(1/4)

=> 1-(2/4)

=> 1-(1/2)

=> (2-1)/2

=> 1/2

Answer:-

The value of Sin⁴θ + Cos⁴ θ for the given problem is 1/2

Used formulae:-

→ Sin⁴θ+ Cos⁴θ = 1-2Sin² θ Cos²θ

→ Sin θ/ Cos θ = Tan θ

→ Tan 45° = 1

→ Sin 45° = 1/√2

→ Cos 45° = 1/√2