To rewrite trigonometric functions into a 'pure power' form (an expression with an exponent of 1), convert all terms to sine and cosine, use the Pythagorean identity (cos²θ = 1 - sin²θ) to eliminate cosine terms, and rearrange to form a quadratic equation in terms of sine. For example, the expression tan²θ + tanθ over cos²θ + 1 can be rewritten as 2sin²θ + sinθ - 1 = 0 by converting tan to sin/cos, finding a common denominator, cross-multiplying, and substituting the identity.
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Added:Here, we want to be able to write a tangent a square data plus tangent to data over cosine a data plus one in the form of two sine a square plus sine a data minus one equals zero.
So, the secret here, we want to convert everybody in term of sine and cosine.
So, we got sine a square data over cosine a square data plus sine [snorts] a data over cosine a square data. So, cosine a square data is the common denominator, which you get a sine a square data plus sine a data is equal one. If I cross multiply, I get sine a square data plus sine a data is equal cosine a square data.
Everybody knows cosine a square data is equal one minus sine a square data.
So, if I substitute and move everybody to the other side, I get two sine a square data and then I get plus sine a data and I get minus one equals zero.
And of course, right after that, cosine cannot be zero.
In case if we solve it, that means data cannot be uh pi over two or three pi over two.
Those are the very important part. Then you be used trigonometric identity to prove or rewrite the equation in trigonometric. You always want to learn material from that experienced person in mathematics. Please follow and subscribe. Thank you.
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