Question

If cot=7/8 , evaluate : (i) (1 + sin⁡θ )(1 - sin⁡θ )/((1 + cos θ) (1 - cosθ)) (ii) 〖cot〗^2 θ .

Answer 1

Answer:

49 / 64

Step-by-step explanation:

Given,

         cotA = 7 / 8

Here, we said to evaluate :

⇒ ( 1 + sinA )( 1 - sinA ) / ( 1 + cosA )( 1 - cosA )

⇒ { 1^2 -( sinA )^2 } / { 1^2 - ( cosA )^2 }

⇒ ( 1 - sin^2 A )( 1 - cos^2 A )  

From the properties of trigonometry :

• 1 - sin^2 A = cos^2 A
• 1 - cos^2 A = sin^2 A

Using these :

⇒ ( cos^2 A ) / ( sin^2 A )

⇒ ( cosA / sinA )^2

⇒ ( cotA )^2                     { We know, cotA = sinA / cosA }

⇒ ( 7 / 8 )^2

⇒ 49 / 64

Answer 2

Step-by-step explanation:

I hope it is helpful to u