Question #b88bf

2 Answers
Oct 4, 2017

See below

Explanation:

To Prove
cottheta+tantheta=sectheta csctheta

L.H.S.
=cottheta+tantheta

because cottheta=costheta/sintheta "and" tantheta=sintheta/costheta

=costheta/sintheta+sintheta/costheta
Take LCM Sinthetacostheta
=(cos^2theta+sin^2theta)/(sinthetacostheta)
=1/(sinthetacostheta)

because 1/sintheta=csctheta ""and" 1/costheta=sectheta

=secthetacsctheta

"see explanation"

Explanation:

"using the "color(blue)"trigonometric identities"

•color(white)(x)cottheta=costheta/sintheta" and "tantheta=sintheta/costheta"

•color(white)(x)cosectheta=1/sintheta" and "sectheta=1/costheta"

•color(white)(x)cos^2theta+sin^2theta=1

rArrcottheta+tantheta

=>costheta/sintheta+sintheta/costheta

=>(cos^2theta+sin^2theta)/(sintheta×costheta)

=>1/(sinthetacostheta)=1/sintheta×1/costheta=csctheta×sectheta