If tan theta =2 evaluate tan theta -cosec theta +sin theta sec theta - Maths - Some Applications of Trigonometry

Question

If tan theta =2 evaluate tan?theta -cosec theta +sin theta sec
theta

Shruti Tyagi · Accepted Answer

Dear student,

Assuming to evaluate is tan2θ-cosecθ+sinθsecθGiven: tanθ=2⇒PerpendicularBase=PB=21In rt ∆ ABC
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5ab5de7910b05%20jpg"
style="width: 350px; height: 223px;">
Pythagoras theoremH2=P2+B2⇒H2=22+12⇒H2=4+1⇒H2=5⇒H=±5⇒H=5                    --[neglectin -ve value]To find tan2θ-cosecθ+sinθsecθ=PB2-HP+PHHB=212-52+25×51=4-52+2=8-5+42=12-52

Regards

If tan theta =2 evaluate tan?theta -cosec theta +sin theta sec theta