Verify the identity.
sin(α + β) / (cos α cos β) = tan α + tan β
Rewrite the numerator on the left side of the identity using one of the sum and difference formulas.

Question

Verify the identity. sin(α + β) / (cos α cos β) = tan α + tan β Rewrite the numerator on the left side of the identity using one of the sum and difference formulas.

SnapAndSolve AI · Accepted Answer

To verify the identity, we start by rewriting the numerator using the sine sum formula:

Sine Sum Formula: sin(α + β) = sin α cos β + cos α sin β

Substitute this into the identity:

sin(α + β) / (cos α cos β) = (sin α cos β + cos α sin β) / (cos α cos β)

Separate the terms:

(sin α cos β) / (cos α cos β) + (cos α sin β) / (cos α cos β)

Simplify each term:

tan α + tan β

Thus, the identity is verified.

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Verify the identity. sin(α + β) / (cos α cos β) = tan α + tan β Rewrite the numerator on the left side of...

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