Question

Solve this question :​

Answer 1

9514 1404 393

Step-by-step explanation:

For proofs of this nature, it often works well to replace everything possible with appropriate equivalents. Here, we'll use sin² to represent sin²(A), and equivalent notation for other trig functions.

We will change the left side to the form of the right side.

`\displaystyle (\tan^2-\cot^2)/(1+\cot^2)=(\sin^2-\cos^2)/(\cos^2)\\\\=((\sec^2-1)-(\csc^2-1))/(\csc^2)\\\\=(\sin^2)(\sec^2-\csc^2)\\\\=(\sin^2)/(\cos^2)-1=(\sin^2-\cos^2)/(\cos^2)\qquad\text{Q.E.D.}`

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The equivalents (identities) used are ...

1+tan² = sec²

1+cot² = csc²

1/csc = sin

sec = 1/cos