tan(2x)+cot(2x)=5
Solution :
tan(2x+cot(2x)=5
sin(2x)/cos(2x)+cos(2x)/sin(2x)=5
multiply both sides by sin(2x)*cos(2x)
sin^2(2x)+cos^2(2x)=5*sin(2x)*cos(2x)
1=5*2*sin(2x)*cos(2x)/2
1=5*sin(4x)/2
sin(4x)=2/5 to be solved
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| Identities of tangent and cotangent | |||||||||
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| Find sin(4x) if : tan(2x)+cot(2x)=5 Solution : tan(2x+cot(2x)=5 sin(2x)/cos(2x)+cos(2x)/sin(2x)=5 multiply both sides by sin(2x)*cos(2x) sin^2(2x)+cos^2(2x)=5*sin(2x)*cos(2x) 1=5*2*sin(2x)*cos(2x)/2 1=5*sin(4x)/2 sin(4x)=2/5 to be solved |
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