Question

7 the question pls explain it's urgent
And thanks for the answer

Answer 1

Ans.) Let △ABC in which  ∠B=90∘

and ∠C=Θ

A/q,

cot Ѳ =BC/AB = 7/8

Let BC = 7k and AB = 8k, where k is a positive real number

According to Pythagoras theorem in △ABC we get.

 

AC2=AB2+BC2

 

AC2=(8k)2+(7k)2

 

AC2=64k2+49k2

 

AC2=113k2

 

AC=113−−−√k

 

sin Ѳ = AB/AC = 8k/113−−−√k=8/113−−−√

and cos Ѳ = BC/AC = 7k/113−−−√k=7/113−−−√

 

(i) (1+sin Ѳ)(1-sinѲ)/(1+cosѲ)(1-cos Ѳ) = (1−sin2Θ)/(1−cos2Θ)

= 1−(8/113−−−√)2/1−(7/113−−−√)2

= {1-(64/113)}/{1-(49/113)} = {(113-64)/113}/{(113-49)/113} = 49/64

 

(ii) cot2Θ=(7/8)2=49/64