[2cos^(3)theta-cos theta],[" (viii) "(sin A+cosec A)^(2)+(cos A+sec A)^(2)=7+tan^(2)A+cot^(2)A]

Prove that (sin theta + "cosec" theta)^(2)+(cos theta + sec theta)^(2)=(7+ tan^(2) theta + cot^(2) theta).

Prove the following identities: (tan theta-cot theta)/(sin theta cos theta)=sec^(2)theta-cos ec^(2)theta=tan^(2)theta-cot^(2)theta

( sin theta + " cosec " theta )^(2) + ( cos theta + sec theta )^(2)=

Prove that: (sin theta-cos ec theta)^(2)+(cos theta-sec theta)^(2)=cot^(2)theta+tan^(2)theta-1

If (cos ^(2) theta - 1) ( 2 sec ^(2) theta) + sec ^(2) theta + 2 tan ^(2) theta = 2 , 0 ^(@) lt theta lt theta lt 90^(@) , then (( "cosec" theta + cos theta))/(( "cosec theta - cos theta)) is equal to :

Prove that (1+ cot theta + tan theta ) ( sin theta - cos theta) = (sec theta )/(cosec^(2) theta) - (cosec theta)/(sec^(2)theta) .

(sin theta+sec theta)^(2)+(cos theta+csc theta)^(2)=(1+cos ec theta sec theta)^(2)

Prove that ((1+cot theta+tan theta)(sin theta-cos theta))/(sec^(3)theta-cos ec^(3)theta)=sin^(2)theta cos^(2)theta

Prove that : (sin theta + sec theta) ^(2) + (cos theta + cosec theta) ^(2) = (1 + sec theta cosec theta) ^(2).