if 4 theta and 5theta are acute angles such that sin5theta =cos4theta, then what is the value of 2cos6theta+sqreroot of3cot6theta
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let this theta be A for simplicity
given➡sin5A=cos4A
sin5A=sin(90°-4A)
5A=90°-4A
5A+4A=90°
9A=90°
A=90/9
A=10°
put this value of theta or A in equation- 2cos6×10+√3cot6×10
2×cos60+√3×cot60
2×1/2+√3×1/√3
1+1=2
hence 2 is the required answer
given➡sin5A=cos4A
sin5A=sin(90°-4A)
5A=90°-4A
5A+4A=90°
9A=90°
A=90/9
A=10°
put this value of theta or A in equation- 2cos6×10+√3cot6×10
2×cos60+√3×cot60
2×1/2+√3×1/√3
1+1=2
hence 2 is the required answer
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