find the value of : (sin2theta+tan2theta),if cosin theta=2524 - Maths - Introduction to Trigonometry

Question

find the value of :
(sin2theta+tan2theta),if cosin
theta=2524

Pronay · Accepted Answer

$\cos ine θ = \frac{25}{24} \Rightarrow \sin θ = \frac{24}{25}$

$\sin^{2} θ + \cos^{2} θ = 1 \Rightarrow \cos^{2} θ = 1 - \sin^{2} θ \Rightarrow \cos θ = \sqrt{1 - {(\frac{24}{25})}^{2}} \Rightarrow \cos θ = \sqrt{\frac{49}{625}} \Rightarrow \cos θ = \frac{7}{25}$

$\tan θ = \frac{\sin θ}{\cos θ} = \frac{(\frac{24}{25})}{(\frac{7}{25})} = \frac{24}{7}$

Consider

$\sin^{2} θ + \tan^{2} θ = {(\frac{24}{25})}^{2} + {(\frac{24}{7})}^{2} = {(24)}^{2} (\frac{1}{625} + \frac{1}{49}) = \frac{576 \times 674}{625 \times 49} = 12.6767$