Question

given that teta =8/7 then evaluate (1+sinteta)*(1-sinteta) /cos teta ​

Answer 1

Question:- Given  tanФ = 8/7 then evaluate (1+sinФ)(1-sinФ)/cosФ

Answer:  7/√113

Step-by-step explanation:

Given,

tanФ = 8/7

Squaring both sides,

tan²Ф = 64/49

Adding +1 both sides,

1 + tan²Ф = 64/49 + 1

1 + tan²Ф = (64 + 49)/49

1 + tan²Ф = 113/49

Taking Square root of both sides

√(1 + tan²Ф) = √113/7

1/√(1 + tan²Ф) = 7/√113

But,  1/√(1 + tan²Ф) = cosФ

cosФ = 7/√113

We know  that,

(a - b)(a + b) = a² - b²

Similarly,

(1 - sinФ)(1 + sinФ) = 1 - sin²Ф

But,

1 - sin²Ф = cos²Ф

Now,

(1 + sinФ)(1 - sinФ)/cosФ

= cos²Ф/cosФ

= cosФ

= 7/√113