Amazing Trigonometry_3

Geometry Level 4

If $\dfrac { \cos { (\alpha -3\theta ) } }{ { { \cos }^{ 3 }\theta } } =\dfrac { \sin { (\alpha -3\theta ) } }{ { \sin }^{ 3 }\theta } = m$ , then find the value of ${ m }^{ 2 }+m\cos { \alpha }$ .

This problem is a part of this set .

The answer is 2.

1 solution

Yashas Ravi
Apr 26, 2019

Assume $α = 0$ for simplicity. Then, the expression becomes:

Since you can replace $sin(θ)$ with $cos(θ)$ , $sin(θ)=cos(θ)$ so $θ=45$ degrees. Then, substitute $45$ degrees for $θ$ and $0$ for $α$ into one of the equal expressions in the problem to get $m=-2$ . Since we assumed $α = 0$ , $cos(α)=1$ so the answer is $(-2)^2 -2(1) = 2$ which is the final answer.

U just can't do that

Abhinav Shripad - 1 year, 4 months ago

Great now prove that this will be true for all , although this a very fine trick to do in competitive exams

Hitesh Yadav - 10 months, 3 weeks ago

Amazing Trigonometry_3

This problem is a part of this set .

The answer is 2.

1 solution

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