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Question

If f(x)=1+sin(90+2x)cos(270+2x)cos(360+4x) then value of tan30f(30)+tan45f(45) is

A
0
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B
13
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C
331
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D
31
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Solution

The correct option is B 13
f(x)=1+sin(90+2x)cos(270+2x)cos(360+4x)

f(x)=1+cos2xsin2xcos4x

f(30)=1sin(2×30)+cos(2×30)cos(4×30)=33
f(45)=1sin(2×45)+cos(2×45)cos(4×45)=0

Now, tan30f(30)+tan45f(45)
=13×(33)+(1×0)=13

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