Tan theta + cot theta =7 find the value of tan square theta + cot square theta?

2 Answers
Feb 18, 2018

The value is #=47#

Explanation:

We need

#tantheta=sintheta/costheta#

#cottheta=costheta/sintheta#

#tantheta*cottheta=sintheta/costheta*costheta/sintheta=1#

Here, we have

#tantheta+cottheta=7#

Squaring both sides

#(tantheta+cottheta)^2=7^2#

#tan^2theta+cot^2theta+2*tantheta*cottheta=49#

#tan^2theta+cot^2theta=49-2*1=47#

Feb 18, 2018

#47#

Explanation:

Note that:

#cot theta = 1 / tan theta#

So writing #t = tan theta# the problem becomes:

Given #t+1/t=7# what is the value of #t^2+1/t^2# ?

Squaring both sides of #t+1/t = 7# we get:

#t^2+2+1/t^2 = 49#

Subtracting #2# from both sides:

#t^2+1/t^2 = 47#