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

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