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The equation sin^-1x-cos^-1x=cos^-1(sqrt...

The equation `sin^-1x-cos^-1x=cos^-1(sqrt3/2)` has

A

no solution

B

one solution

C

two solutions

D

more than two solutions

Text Solution

Verified by Experts

We have,
`3^(x-1)+5^(x-1)=34`
`implies 3^(x-1)+5^(x-1)=3^(2)+5^(2) impliesx-1=2 implies x=3`
So, the given equation has just one solution.
ALITER The total number of solutions is same as the number of points of intersection of the curves
`y=3^(x-1)+5^(x-1)` and y=34

It is evident from the graph that these two curves intersect at exactly one point. Hence, the given equation has exactly one solution.
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