If `sintheta +cos theta =m` and `sec theta + cosec theta =n` then `n(m+1)(m-1)` equals

If sin theta+ cos theta = p and sec theta + cosec theta = q ; show that q(p^2-1) = 2p

If cos ec theta - sin theta = m and sec theta - cos theta = n, then show that (m ^(2) n ) ^(2//3) + (mn ^(2)) ^( 2//3) = 1.

If cosectheta-sintheta=m a n d sectheta-costheta=n ,"eliminate"theta

From algebra we know that if ax^(2) +bx + c=0 , a( ne 0), b, c int R has roots alpha and beta then alpha + beta=-b/a and alpha beta = c/a . Trignometric functions sin theta and cos theta, tan theta and sec theta, " cosec " theta and cot theta obey sin^(2)theta + cos^(2)theta =1 . A linear relation in sin theta and cos theta, sec theta and tan theta or " cosec "theta and cos theta can be transformed into a quadratic equation in, say, sin theta, tan theta or cot theta respectively. And then one can apply sum and product of roots to find the desired result. Let a cos theta, b sintheta=c have two roots theta_(1) and theta_(2) . theta_(1) ne theta_(2) . The vlaue of cos(theta_(1) + theta_(2)) is a and b not being simultaneously zero)

From algebra we know that if ax^(2) +bx + c=0 , a( ne 0), b, c R has roots alpha and beta then alpha + beta=-b/a and alpha beta = c/a . Trignometric functions sin theta and cos theta, tan theta and sec theta, " cosec " theta and cot theta obey sin^(2)theta + cos^(2)theta =1 . A linear relation in sin theta and cos theta, sec theta and tan theta or " cosec "theta and cos theta can be transformed into a quadratic equation in, say, sin theta, tan theta or cot theta respectively. And then one can apply sum and product of roots to find the desired result. Let a cos theta, b sintheta=c have two roots theta_(1) and theta_(2) . theta_(1) ne theta_(2) . The value of cos(theta_(1)-theta_(2)) is (a and b not being simultaneously zero)

From algebra we know that if ax^(2) +bx + c=0 , a( ne 0), b, c in R has roots alpha and beta then alpha + beta=-b/a and alpha beta = c/a . Trignometric functions sin theta and cos theta, tan theta and sec theta, " cosec " theta and cot theta obey sin^(2)theta + cos^(2)theta =1 . A linear relation in sin theta and cos theta, sec theta and tan theta or " cosec "theta and cos theta can be transformed into a quadratic equation in, say, sin theta, tan theta or cot theta respectively. And then one can apply sum and product of roots to find the desired result. Let a cos theta, b sintheta=c have two roots theta_(1) and theta_(2) . theta_(1) ne theta_(2) . The values of tan theta_(1) tan theta_(2) is (given |b| ne |c|)

If cosectheta-sintheta=m" and " sectheta-costheta=n , elimnate theta .

Let l= sin theta, m=cos theta and n=tan theta . If theta=5 radian, then :

If tan theta +sin theta =m and tan theta -sin theta =n then prove m^2-n^2=4sqrt(mn)

If cos e c\ theta+cottheta=m and cos e c\ theta-cottheta=n , prove that m n=1