Prove that:`|(x.sintheta,costheta),(-sintheta,-x,1),(costheta,1,x)|=-x^3`

Show that: |(sintheta,costheta),(-costheta,sintheta)| =1

Prove that (frac(1+sintheta)(1+costheta)) + (frac(1-sintheta)(1-costheta)) = 2(cosec^2theta-cottheta)

int((sintheta+costheta))/sqrt(sin2theta)"d"theta=

Prove that (frac(1+sintheta-costheta)(1+sintheta+costheta))=sqrt(1-costheta)/sqrt(1+costheta)

Prove that : (sin theta)/(1 - costheta) = cosec theta + cot theta

(sintheta+sin 2theta)/(1+costheta+cos2theta)=

Prove that (frac(sintheta-2sin^3theta)(2cos^3theta-costheta))=tantheta

Prove the following: (frac(sin^3theta+cos^3theta)(sintheta+costheta))+(frac(sin^3theta-cos^3theta)(sintheta-costheta))=2

sintheta/(1-cottheta)+costheta/(1-tantheta)=

Answer the following questions.If A=[[costheta,sintheta],[-sintheta,costheta]] ,prove that A^n=[[cos ntheta,sin ntheta],[-sin ntheta,cos ntheta]] , for all n in N