How do you find the exact values of sin2u, cos2u, tan2u using the double angle values given cotu=-4, (3pi)/2<u<2pi?

1 Answer
Feb 13, 2017

sin2u=-8/17, cos2u=15/17 and tan2u=-8/15

Explanation:

As cotu=-4, tanu=-1/4

:.tan2u=(2tanu)/(1-tan^2u)=(2xx(-1/4))/(1-(-1/4)^2)

= (-1/2)/(1-1/16)=(-1/2)/(15/16)

= -1/2xx16/15=-8/15

Therefore sec2u=sqrt(1-tan^2 2u)

= sqrt(1-(-8/15)^2)=sqrt(1+64/225)=sqrt(289/225)=17/15

We have kept it positive as (3pi)/2 < u < 2pi and hence 3pi < 2u < 4pi,

but as tan2u=-8/15, 2u must be in Q4 and sec2u > 0.

therefore cos2u=1/(sec2u)=15/17

and sin2u=tan2uxxcos2u=-8/15xx15/17=-8/17