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Question

Shamita teaches a2+b2 number of underprivileged children of her locality every Sunday, where a cosθ+bsinθ=2 and a sinθbcosθ= 3. The number of children taught by Shamita every Sunday is

A
5
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B
7
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C
11
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D
13
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Solution

The correct option is D 13
acosθ+bsinθ=2 .....(i)

asinθbcosθ=3 ......(ii)

Squaring and then adding (i) & (ii), we get

a2(sin2θ+cos2θ)+b2(sin2θ+cos2θ)+2absinθcosθ2absinθcosθ=4+9

a2+b2=13 [sin2θ+con2θ=1]

[From (i) and (ii)]

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