Show that the equation `sec theta + cosec theta =c` has two roots between 0 and `2pi` if `2 lt c^(2) lt 8`

Show that the equation , sec theta + "cosec" theta = c has two roots between 0 and 2pi , if c^2 lt 8 and four root if c^(2) gt 8 .

If the equation "sec" theta + "cosec" theta =c has real roots between 0 and 2pi , then

If the equation "sec" theta + "cosec" theta =c has real roots between 0 and 2pi , then

Consider the equation sec theta +cosec theta=a, theta in (0, 2pi) -{pi//2, pi, 3pi//2} If the equation has no real roots, then

Value(s) of theta satisfying the equation sin 7 theta = sin 4 theta - sin theta , where 0 lt theta lt (pi//2) , are

The number of real roots of the equation cosec theta + sec theta-sqrt(15)=0 lying in [0, pi] is

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 values of tan theta_(1) tan theta_(2) is (given |b| ne |c|)

The number of real roots of the equation csc theta+sec theta-sqrt(15)=0ling in [0,pi] is.6 (b) 8 (c) 4 (d) 0