Question

sin⁴θ - cos⁴θ = 
If tanθ + secθ = 8 , then the value of secθ - tanθ =​

Answer 1

Answer:

secθ - tanθ = 4 -----> (1)

Multiplying and dividing by secθ +tanθ

= secθ - tanθ × secθ +tanθ/secθ +tanθ

= sec²θ - tan²θ/secθ + tanθ = 4

we know that --> sec²θ - tan²θ = 1

1/secθ + tanθ = 4

therefore ,

secθ + tanθ = 1/4 ----> (2)

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Adding equations (1) and (2) :-

secθ - tanθ = 4

secθ + tanθ = 1/4

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2secθ = 4 + 1/4

2secθ = 17/4

secθ = 17/4*2

= 17/8

we know that

cosθ = 1/secθ

= 1/(17/8)

= 8/17

Proved !

Answer 2

Answer:

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