Given that A-B are positive acute angle and - 3 sin2A-sin2B- 3 sin 2 A- sin 2 B- 3 -1 2- then A or B may take the values -

The correct option is B 15 ^ o the above question is extremely simple to do, and #160;A=15, B=30 degreeto solve this, simply write sin^2A and sin^2B in ...

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Standard XII

Mathematics

One - One function

Given that A,...

Question

Given that A,B are positive acute angle and $\sqrt{3} s i n 2 A = s i n 2 B & \sqrt{3} {s i n}^{2} A + {s i n}^{2} B = \frac{\sqrt{3} - 1}{2}$ , then A or B may take the value(s) ?

15^{o}

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30^{o}

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45^{o}

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75^{o}

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Solution

The correct option is B

15^{o}

the above question is extremely simple to do, and A=15, B=30 degree

to solve this, simply write sin^2A and sin^2B in the second equation in terms of cos2A and cos2B (using the formula cos2x=1-2sin^2x).

so, the second equation becomes: √3cos2A=2-cos2B   …...(2)

while the first equation is given as:√3sin2A=sin2B …...(1)

squaring and adding both the equations, we get: 3= 4+1-4cos2B

or, 1/2=cos2B=cos60

2B=60 or B=30

from (1), √3sin2A=sin2B=sin60=√3/2

or sin2A=1/2=sin30

or, 2A=30

or, A=15 degree

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Given that A,B are positive acute angle and √3sin2A=sin2B&√3sin2A+sin2B=√3−12, then A or B may take the value(s) ?

Given that A,B are positive acute angle and $\sqrt{3} s i n 2 A = s i n 2 B & \sqrt{3} {s i n}^{2} A + {s i n}^{2} B = \frac{\sqrt{3} - 1}{2}$ , then A or B may take the value(s) ?