If `theta_C` is the critical angle and `theta_P` is the polarizing angle for a transparent medium, show that `sin theta_C = cot theta_P`

If 8theta = pi show that cot 7theta+cot theta = 0

Suppose theta is the polarizing angle for a transparent medium and the speed of light in that medium is v. (Then according to Brewster law )

Solve : cos p theta = sin q theta.

If tan theta + cot theta = 2 find sin theta ?

If theta is an acute angle and tan theta + sec theta = 1.5 , find sin theta, tan theta and sec theta .

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 theta is an acute angle and tantheta+cottheta=2, find the value of tan^7theta+cot^7theta .

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)

Prove that sin(2theta)/(1-cos2theta)=cot theta