If a2 - 2a cosx + 1 =674 and tan (x/2) = 7 and the integral value of a is - Maths - Trigonometric Functions

Question

If a2 - 2a cosx + 1 =674 and tan (x/2) = 7 and the
integral value of a is 5k, then k is _________

Ankush Jain · Accepted Answer

Given, a2 - 2a cos x + 1 =674 (1) and tan (x/2) = 7 $W e k n o w t h a t \cos x = \frac{1 - \tan^{2} \frac{x}{2}}{1 + \tan^{2} \frac{x}{2}} \Rightarrow \cos x = \frac{1 - (7)^{2}}{1 + (7)^{2}} \Rightarrow \cos x = \frac{- 48}{50} = \frac{- 24}{25}$ Also, a = 5k So, (1) becomes, $25 k^{2} - 2 (k) (\frac{- 24}{5}) = 673 \Rightarrow 125 k^{2} + 48 k = 3365 \Rightarrow 125 k^{2} + 48 k - 3365 = 0 \Rightarrow 125 k^{2} + 673 k - 625 k - 3365 = 0 \Rightarrow k (125 k + 673) - 5 (125 k + 673) = 0 \Rightarrow (k - 5) (125 k + 673) = 0 \Rightarrow k = 5, \frac{- 673}{125}$

If a2 - 2a cosx + 1 =674 and tan (x/2) = 7 and the integral value of a is 5k, then k is _________.

If a² - 2a cosx + 1 =674 and tan (x/2) = 7 and the integral value of a is 5k, then k is _________.