Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If
cos
−
1
x
a
+
cos
−
1
y
b
=
θ
\cos^{-1} \frac{x}{a} + \cos^{-1} \frac{y}{b} = \theta
cos
−
1
a
x
+
cos
−
1
b
y
=
θ
, then show that
x
2
a
2
+
y
2
b
2
−
2
x
y
a
b
cos
θ
=
sin
2
θ
\frac{x^2}{a^2} + \frac{y^2}{b^2} - \frac{2xy}{ab} \cos \theta = \sin^2 \theta
a
2
x
2
+
b
2
y
2
−
ab
2
x
y
cos
θ
=
sin
2
θ
.
Browse the problem library