Question

Cos25°+sin25°=p, cos50°=?

Answer 1

Please see the attachment

Answer 2

Answer:

$\sqrt{2-p^2}$

Step-by-step explanation:

We are given that

$cos25^{\circ}+sin 25^{\circ}=p$

We have to find the value of $cos50^{\circ}$

Squaring on both  sides

$(cos 25^{\circ}+sin25^{\circ})^2=p^2$

$(a+b)^2=a^2+b^2+2ab$

Using this identity

$cos^225^{\circ} + sin^225^{\circ}+2 cos 25^{\circ}sin25^{\circ}=p^2$

We know that $sin^2\theta+cos^2\theta=1$ and $sin2\theta=2sin\thetacos\theta$

Using these identities

$1+sin50^{\circ}=p^2$

$sin 50^{\circ}=p^2-1$

$cos \theta=\sqrt{1- sin^2\theta}$

$Cos 50^{\circ}=\sqrt {1-(p^2-1)}$

$cos 50^{\circ}=\sqrt{1-p^2+1}=\sqrt{2-p^2}$