`(1+tan^(2)theta)=sec^(2)theta`

If theta=45^(@) then (tan^(2)theta-1)/(sec^(2)theta)=

sec^(6)theta=tan^(6)theta+3tan^(2)theta sec^(2)theta+1

sec^(6)theta=tan^(6)theta+3tan^(2)theta sec^(2)theta+1

Prove :sec^(6)theta=tan^(6)theta+3tan^(2)theta sec^(2)theta+1

sqrt((1-cos^(2)theta)sec^(2)theta)=tan theta

(tan^(2)theta)/(sec theta+1)=

Eliminate theta from the relations a sec theta=1-b tan theta,a^(2)sec^(2)theta=5+b^(2)tan^(2)theta

Find the values of theta in the interval (-(pi)/(2),(pi)/(2)) satisfying the equation (1-tan theta)(1+tan theta)sec^(2)theta+2^(tan^(2)theta)=0

(1+2sin theta+sin^(2)theta)/(cos^(2)theta)=(sec theta+tan theta)/(sec theta-tan theta)

Prove: (tan^(3)theta-1)/(tan theta-1)=sec^(2)theta+tan theta .