tan^2theta+6=sec^2theta+5
To solve the equation tan^2theta + 6 = sec^2theta + 5, we can use the trigonometric identity relating secant and tangent.
The identity is: sec^2theta = 1 + tan^2theta
Substituting this identity into the equation, we get:
tan^2theta + 6 = (1 + tan^2theta) + 5
Expanding the equation:
tan^2theta + 6 = 1 + tan^2theta + 5
Combining like terms:
tan^2theta + 6 = tan^2theta + 6
As we can see, both sides of the equation are identical. This means that the equation is satisfied for any value of theta. In other words, the equation has an infinite number of solutions.
Are we solving for Ø ?
tan^2 Ø +6 = sec^2 Ø + 5
sin^2 Ø/cos^2 Ø + 6 = 1/cos^2 Ø + 5
times cos^2 Ø
sin^2 Ø + 6cos^2 Ø = 1 + 5 cos^2 Ø
sin^2 Ø + cos^2 Ø = 1
1 = 1
ahh, it was an identity, thus true for all values of Ø, except Ø = 90° , 270° , 450° ..... or 90° + 180k , where k is an integer.