Assertion: If cot^-1(√(cosα))-tan^-1(√(cosα))=x, then sinx=tan^2 (α)/(2) Reason: tan^-1 x-tan^-1

step 1 So we can write this 10 inverse 1 upon under root cost alpha minus 10 inverse root cause alpha e

Assertion: If cot^-1(√(cosα))-tan^-1(√(cosα))=x, then...

Assertion: If $\cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x$,
then $\sin x=\tan ^{2} \frac{\alpha}{2}$
Reason: $\tan ^{-1} x-\tan ^{-1} y=\tan ^{-1}\left(\frac{x-y}{1+x y}\right)$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Difference Formula for Inverse Tangent

This formula, which states that tan?¹(x) - tan?¹(y) = tan?¹((x - y)/(1 + xy)) under appropriate conditions, is a pivotal tool in simplifying expressions involving differences of inverse tangent functions. It enables one to combine two inverse trigonometric expressions into a single expression, thereby aiding in the proof or derivation of more complex trigonometric identities.

Inverse Trigonometric Functions

These functions, including arctan and arccot, serve as the inverses of the tangent and cotangent functions respectively. They allow one to compute an angle corresponding to a given trigonometric ratio, and their properties facilitate the transformation of trigonometric expressions into forms that are more manageable for analysis and proof of identities.

Half-Angle Trigonometric Identities

Half-angle formulas link trigonometric functions of an angle to functions of half that angle. They are particularly useful in expressing complex trigonometric expressions in terms of simpler functions, such as writing the sine of an angle in terms of the tangent of half the angle. This simplification is essential in validating identities where angles are bisected, as seen in the relationship between sin x and tan²(?/2) in the given assertion.

Transcript

Please give Ace some feedback