If tan A = root 3+1/root 3-1, then what is the value of cos 2A + (2 + root 3)sin - Maths - Trigonometric Functions

Question

If tan A = root 3+1/root 3-1, then what is the value of cos 2A + (2
+ root 3)sin 2A?

Lovina Kansal · Accepted Answer

Dear
studentGive: tanA=3+13-1tanA=3+13-1×3+13+1tanA=3+123-1tanA=4+232tanA=2+3=PBBy Pythagoras theorem,H=P2+B2=2+32+12=4+3+43+1=8+43=22+3So, sinA=PH=2+322+3=12cosA=BH=122+3Thus,cos2A+2+3sin2A=1-2sin2A+2+32 sinA cosA=1-2122+2+32×12×122+3=1-12+2+3×122+3=1-12+12=1

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If tan A = root 3+1/root 3-1, then what is the value of cos 2A + (2 + root 3)sin 2A?