Question

Given cot0=7/8 then evaluate 1+sin0/cos0

Answer 1

Answer:

(√113 + 8)/7

Step-by-step explanation:

= > cot0 = 7/8

= > base/height = 7/8

So let the base be 7a and height be 8a.

Using Pythagoras theorem,

= > hypotenuse² = (7a)² + (8a)²

= > hypotenuse² = 49a²+64a² = 113a²

= > hypotenuse = √113a² = a√113

Therefore,

= > 1 + sin0 = 1 + (height/hypo.)

= > 1 + 8a/a√113

= > (√113 + 8)/√113

= > cos0 = base/hypo. = 7a/a√113 = 7/√113

Thus,

= > (1 + sin0)/cos0

= > (√113 + 8)/7

Answer 2

Answer:-

cot 0=adjacent side/opposite side=7/8

According to Pythagoras theorem,

AC²=AB²+BC²=√49+64=√113

sin 0=opposite side/hypotenuse side=8/√113

cos 0=adjecent side / hypotenuse side=7/√113

thus,

1+sin 0/cos0=1+8/√113/7/√113=√113+8/7