The Pythagorean identities are sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ. Then the correct options are B, C, and E.
It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.
We know that
[tex]\rm H^2 = P^2+B^2[/tex]
Divide the equation by H², then we have
[tex]\rm\dfrac{P^2}{H^2}+\dfrac{B^2}{H^2} = 1 \\\\\sin ^2 \theta + \cos ^2 \theta = 1[/tex]
Similarly, the equation is divided by P² and B², then we have
[tex]\rm 1 + \tan ^2 \theta = \sec ^2 \theta \\\\1 + \cot ^2 \theta = cosec ^2 \theta[/tex]
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
