Answer :
Given that cosθ = 14/15, tanθ can be found by using the Pythagorean identity. After calculating sinθ and using the ratio of sine to cosine, tanθ is determined to be √29 / 14.
To find the value of tanθ given that cosθ = 14/15, we will use the Pythagorean identity that relates the sine and cosine of an angle. According to the Pythagorean theorem, sin2θ + cos2θ = 1. Since cosθ is given as 14/15, we can solve for sinθ as follows:
cos2θ = (14/15)2
sin2θ = 1 - cos2θ
sin2θ = 1 - (14/15)2
sin2θ = 1 - (196/225)
sin2θ = (225/225) - (196/225)
sin2θ = 29/225
sinθ = ±√(29/225)
We take the positive square root because the range of cosine where it is positive includes the first and fourth quadrants where sine is also positive or zero. Then, to find tanθ, which is the ratio of sine over cosine, we calculate:
tanθ = sinθ / cosθ
tanθ = √(29/225) / (14/15)
tanθ = √(29/225) * (15/14)
tanθ = √29 / 14
