Trigonometry> Solve: (sin theta+cosec theta)^2 + (cos t...

Solve: (sin theta+cosec theta)^2 + (cos theta +sec theta)^2- (tan^2 theta + cot ^2 theta)^2

Naveen Shankar , 8 Years ago

Grade 11

5 Answers

Naveen Shankar

Last Activity: 8 Years ago

this is the question :: Solve: (sin theta+cosec theta)^2 + (cos theta +sec theta)^2 - (tan^2 theta + cot ^2 theta)

Ajay

Last Activity: 8 Years ago

What needs to be solved here ? The question is incomplete....................................................................

Approved

Naveen Shankar

Last Activity: 8 Years ago

i got it open the bracket and simplify and get the answer as 5 …..............................................

Saravanan

Last Activity: 8 Years ago

i don’t know how to do this...............................................................................................

Amartya

Last Activity: 7 Years ago

See, Let`s solve the first bracket . Sin ^2 theta + cosec^2 theta +2sin.cosec.2 bracket =cos^2 theta +sec^2theta +2cos.sec3 bracket= -tan^2theta -cot^2 theta .Now , Sin^2theta +cos^2theta =1__________(1)2.sin.cosec=1___________(2)2.cos.sec=1_______________(3)Then ,-tan^2theta = -sin^2 theta ÷cos^2 theta _(5)-cot^2theta= -cos^2theta ÷sin^2 theta_(6)Cosec^2theta=1÷sin^2theta_(7)Sec^2theta =1÷cos^2theta_(8)Adding 5678 together ,we get 1-cos^2theta ÷sin^2theta + 1-sin^2theta÷cos^2thetaNow let`s look at identities sin^2theta +cos^2theta=1We get , 1-cos^2theta =sin^2theta and 1-sin^2theta=cos^thetaPutting these two values above we get ,Sin^2theta÷sin^2theta + cos^2theta÷cos^2theta.Which is 1+1 Now add (1) (2) (3) with above result of above which is 1+1+1+1+1=5Answer