71Sum 1 is also having RHS wrong.
By the way, Whatever be that sum, You just convert tan-1 x into sin-1 x/√(1+x2) and apply the formula. You'll get the required answer!
1.If sin-1x + tan-1x =/2
then 2x2 + 1 =
a)√5 b)[sqrt(]5-1)/2 c)2 d)none
2.If cos-1x/2 + cos-1y/3 =0,
9x2 - axycosθ + by2=csin2θ
prove that a-b+c=44.
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2 Answers
622nd one..
I think what you have is theta not 0 in the RHS
cos-1x/2 + cos-1y/3 = θ
\frac x2\frac y3-\sqrt{1-x^2/4}\sqrt{1-y^2/9}=cos\theta \\\Rightarrow xy-6\cos\theta=\sqrt{4-x^2}\sqrt{9-y^2} \\\Rightarrow x^2y^2+36\cos^2\theta-12xy\cos\theta=36+x^2y^2-9x^2-4y^2 \\\Rightarrow=36\sin^2\theta=9x^2+4y^2-12xy\cos\theta
Compare it with the given 2nd equation....
a=12, b=4 and c=36
hence proved..
71