if cos theta =7/13, where 0<theta<pi/2, fin the value of cos2theta
If you mean to find the value of cos(2θ) given cos(θ)=7/13, then use the double angle formula:
cos(2θ)=cos²(θ)-sin²(θ)
where:
sin²(θ)
=(1-cos²(θ))
=120/169
To find the value of cos(2θ), we can use the double-angle formula for cosine:
cos(2θ) = 2cos^2(θ) - 1
Given that cos(θ) = 7/13, we can square this value to obtain cos^2(θ):
cos^2(θ) = (7/13)^2 = 49/169
Substituting this value into the double-angle formula, we can find cos(2θ):
cos(2θ) = 2(49/169) - 1
= 98/169 - 1
= (98 - 169)/169
= -71/169
Therefore, the value of cos(2θ) is -71/169.