Prove: `(sin phi - cos phi) ^(2) =1 - sin 2 phi. `

Solve 2 sin ^(2) phi = sin phi, ( 0^(@) le phi lt 360^(@)).

Prove that sin^(2)phi(1+cot^(2)phi)=1

Evaluate the following limits (i) lim_(x to (pi)/(2)) tan^(2) x [sqrt(2 sin^(2) x + 3 sin x + 4) - sqrt(sin^(2) x + 6 sin x + 2)] (ii) lim_(theta to 0) (sqrt(1 + sin 3 theta) -1)/(ln(1 + tan 2theta)) (iii) lim_(x to 0) (sqrt(1 + x) - ""^(3)sqrt(1 + x))/(x) (iv) lim_(phi to 0) (8)/(phi^(8)) (1 - cos (phi^(2))/(2) - cos (phi^(2))/(4) + cos (phi^(2))/(2). cos (phi^(2))/(4))

If int(2sin2phi-cosphi)/(6-cos^(2)phi-4sinphi)dphi=p" ln "|sin^(2)phi-4sinphi+5|+qtan^(-1)(sinphi-r)+C then p+q+r equal to:

If theta-phi=pi/2, prove that, [(cos^2 theta,cos theta sin theta),(cos theta sin theta,sin^2 theta)] [(cos^2 phi,cos phi sin phi),(cos phi sin phi,sin^2 phi)]=0

If theta-phi=pi/2, prove that, [(cos^2 theta,cos theta sin theta),(cos theta sin theta,sin^2 theta)] [(cos^2 phi,cos phi sin phi),(cos phi sin phi,sin^2 phi)]=0

Prove that cos 2 theta cos 2 phi + sin ^(2) ( theta - phi) -sin ^(2) (theta + phi) = cos ( 2 theta + 2 phi).

If sin theta is G.M. of sin phi and cos phi, then prove that cos 2 theta = 2 cos ^(2) ((pi)/(4) + phi).

(sin (theta + phi))/( sin theta cos phi) = cot theta tan phi +1.

If a = cos theta + isin theta , b = cosphi + isinphi , c = cos psi + i sin psi and a/b+b/c+c/a=2 then sin(theta-phi)+sin(phi-psi)+sin(psi-theta) equals