Solutions of `sec qx + sec px = 0` form AP with common difference

Solution of secqx+secpx=0 form AP with common difference

If tan px = cot qx , then the solutions are in A.P. with common difference

If tan px=cot qx, then the solutions are in A.P.with common difference

Solutions of the equations "cos"^(2) ((1)/(2) px)+ "cos"^(2) ((1)/(2) qx) = 1 form an arithmetic progression with common difference

Solutions of the equations "cos"^(2) ((1)/(2) px)+ "cos"^(2) ((1)/(2) qx) = 1 form an arithmetic progression with common difference

Given pnepmq . Show that the solutions of cosPtheta+cosqtheta=0 form two series each of which is in A.P . Find also the common difference of each A.P .

Let a_(1) ,a_(2),cdots , a_(n) be an A.P. with common difference pi//6 and assume sec a_(1) sec a_(2)+sec a_(2) sec a_(3) + cdots + sec a_(n-1) sec a_(n)=k ( tan a_(n) - "tan" a_(1) ) Then find the value of k.