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Prove that (sinalpha+cosalpha)(tanalpha+...

Prove that `(sinalpha+cosalpha)(tanalpha+cotalpha)=secalpha+"cosec"alpha`

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(sinalpha + cosalpha)(tanalpha + cotalpha) = secalpha + cosecalpha

Prove that : (sinalpha+cosalpha)(tanalpha+cotalpha)=secalpha+"cosecα" .

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(sinalpha+secalpha)^(2)+(cosalpha+cosecalpha)^(2)=(K+secalphacosecalpha)^(2) , then K = ?

If tantheta = (sinalpha-cosalpha)/(sinalpha+cosalpha), then (A) sin alpha-cos alpha=+-sqrt(2) sin theta (B) sinalpha+cosalpha=+-sqrt(2) cos theta (C) cos2theta=sin2alpha (D) sin2theta+cos2alpha=0

Prove that : 1+(cot^(2)alpha)/(1+"cosec"alpha)="cesec"alpha

A square of side a lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle alpha(0ltalphaltpi/ 4) with the positive direction of x-axis. equation its diagonal not passing through origin is (a) y(cosalpha+sinalpha)+x(sinalpha-cosalpha)="alpha(b)y(cosalpha+sinalpha)+x(sinalpha+cosalpha)=alpha(c)y(cosalpha+sinalpha)+x(cosalpha-sinalpha)=alpha(d)y(cosalpha-sinalpha)-x(sinalpha-cosalpha)=alpha

If intsinx/(sin(x-alpha))dx=Ax+Blogsin(x-alpha)+C , then value of (A,B) is (A) (-sinalpha,cosalpha) (B) (-cosalpha,sinalpha) (C) (sinalpha,cosalpha) (D) (cosalpha,sinalpha)

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) then show that sinalpha+cosalpha=sqrt(2)costheta .