Q1: Given sin(x+22)° = cos(2x−7)°
Using the concept of Right triangles and Trigonometric ratios, we can use a formula given as follows :-
If, sin(A) = cos(B). Then we must have A + B = 90 degrees.
We have sin(x+22)° = cos(2x−7)°
Then it must be true that (x+22)° + (2x−7)° = 90 degrees.
(x + 22) + (2x - 7) = 90
3x + 15 = 90
3x + 15 - 15 = 90 - 15
3x = 75
[tex] \frac{3x}{3} =\frac{75}{3} \\\\x = 25 \;degrees [/tex]
Hence, x = 25 degrees is the final answer.
Q2: Given cos(x) = 1213 and sin(x) = 513.
It says to find ratio of tan(x).
Using the concepts of Trigonometric ratios, We can the formula that relates all three functions i.e. sin(x), cos(x), and tan(x).
tan(x) = [tex] \frac{sin(x)}{cos(x)} [/tex]
We can plug the given values in the formula.
[tex] tan(x) = \frac{513}{1213} [/tex] is the final answer.
