simplify
`tan^2theta(cosec^2theta-1)`

(1+tan^2theta) sin^2theta

Prove that : (i) 1+(cos^(2)theta)/(sin^(2)theta)-"cosec"^(2)theta=0 (ii) (1+tan^(2)theta)/("cosec"^(2)theta)=tan^(2)theta

If cos theta= -1/2 and pi < theta < (3pi)/2 then find the value of 4tan^2 theta- 3cosec^2 theta

Simplify: (1+tan^(2)theta)(1-sintheta)(1+sintheta)

If "cosec" theta = sqrt5 , find the value of : 2+1/(sin^2theta)-(cos^2theta)/(sin^2theta)

Without expanding show that: = |(cose c^2theta,cot^2theta,1),(cot^2theta,cosec^2theta,-1) ,(42 ,40, 2)| =0

Prove that cos^(2)theta("cosec"^(2)theta-cot^(2)theta)=cos^(2)theta .

Without expanding show that: =|[cose c^2theta,cot^2theta,1],[cot^2theta,cosec^2theta,-1],[ 42, 40, 2]|=0

If sin theta+cosec theta=2 , then find the value of sin^(20)theta+cosec^(20)theta .

Statement 1: tan^(2)(sec^(-1)2)+cot^(2)(cosec^(-1)3)=11 . Statement -2 :tan^(2)theta+sec^(2)theta=1=cot^(2)theta+cosec^(2)theta