Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
The right triangle's three sides are as follows:
- Hypotenuse (the longest side) (the longest side)
- Perpendicular (opposite side to the angle) (opposite side to the angle)
- Base (Adjacent side to the angle) (Adjacent side to the angle)
If 1 + sin2 θ = 3 sin θ cos θ, then prove that tan θ = 1 or ½.
If 1 + sin2 θ = 3 sin θ cos θ, then it is proved that tan θ = 1 or ½. In a right triangle, the tangent of an angle is the ratio of the length of the adjacent side to the length of the opposite side. It is written as tan θ = opposite/adjacent.