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Trigonometric Ratios of Allied Angles

39. If cos θ ...

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39. If cos θ = 5/13, then find the value of θ.

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{sin}^{- 1} \frac{3}{5} + {cos}^{- 1} \frac{12}{13} = {cos}^{- 1} \frac{a}{b}

.
Find the value of

a + b

.

sin A = \frac{5}{13}

cos A = \frac{5}{13}

. Find the value of all other trigonometric ratios.

Q. If value of cos(B) is 5/13, then find the value of tan(B).

cos A = \frac{5}{13}

and A is not in first quadrant, then find the value of

\frac{sin A - cos A}{tan A + 1}

{sin}^{- 1} (\frac{12}{13}) + {cos}^{- 1} (\frac{4}{5}) + {tan}^{- 1} (\frac{63}{16}) = a π

.
Find the value of

a

.

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