Question #b88bf

2 Answers
Pankaj Solanki
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#

Jim G. · Chirag Mehta
Oct 4, 2017

#"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#

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