Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

MathematicsTrigonometric Ratios & IdentitiesConditional identitiesHard3 minQB

MathematicsHardmultiple choice

If $x = sin (α - β) sin (γ - δ), y = sin (β - γ) sin (α - δ)$ , and $z = sin (γ - α) sin (β - δ)$ , which identities hold?

Answer:

A, D

Solution:

Product-to-sum identities give $x + y + z = 0$ . Then the standard cubic factorization gives $x^{3} + y^{3} + z^{3} = 3 x yz$ .

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Conditional identities

⏱ 3mℹ️ Source: QB

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