`c o s e c(pi/4+theta/2)c o s e c(pi/4-theta/2)=2sectheta`

Prove that: {1+cottheta-s e c(pi/2+theta)}{1+cottheta+s e c(pi/2+theta)}=2cottheta

If tan theta=1/sqrt7 ,then (c o s e c^2theta-sec^2theta)/(c o s e c^2theta+sec^2theta)=?

Match the following . {:((1) tan(pi/4+theta)-tan(pi/4-theta)=,(a) 1),((b)tan(pi/4+theta)+cot(pi/4+theta)=,(b)4sec^(2)2theta),((c)tan(pi/4+theta).tan(pi/4-theta)=,(c)2sec2theta),((d)cosec^(2)(pi/4+theta)cosec^(2)(pi/4-theta)=,(d)2tan2theta):}

Prove that: ("cos"(2pi+theta)"c o s e c"(2pi+theta)"tan"(pi//2+theta))/("sec"(pi//2+theta)costheta"cot"(pi+theta))=1

Prove that: 2s e c^2theta-s e c^4theta-2cos e c^2theta+cos e c^4theta=(1-t a n^8theta)/(t a n^4theta)

If acottheta+b"c o s e c"theta=p and bcottheta+a"c o s e c"theta=q , then p^2-q^2= (a) a^2-b^2 (b) b^2-a^2 (c) a^2+b^2 (d) b-a

The minimum value of (sintheta+c o s e ctheta)^2+(costheta+sectheta)^2=

tan ((pi)/(4) + (theta)/(2)) + tan ((pi)/(4) -(theta)/(2)) is equal to ............... A) sec theta B) 2 sec theta C) sec "" (theta)/(2) D) -2 sec theta

If theta is an acute angle and t a ntheta=1/(sqrt(7)) , then the value of (cos e c^2theta-sec^2theta)/(cos e c^2theta+sec^2theta) is a. 3//4 b. 1//2 c. 2 d. 5//4

If t a n(pi//4+theta)+t a n(pi//4-theta)=a , then t a n^2(pi//4+theta)+t a n^2(pi//4-theta) = (a) a^2+1 (b) a^2+2 (c) a^2-2 (d) none of these