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The value of tan(alpha+beta) given sin(alpha)=40/41 and sin(beta)=15/17 and cos(∝ + β)= -528/697 and sin(∝ + β)= 455/679

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Answer

Tan (∝ + β) = -455/528

Explanation

Tan (∝ + β) = ?

Given:

Sin ∝ = 40/41

Sin β = 15/17

Cos (∝ + β) = -528/697

Sin (∝ + β) = 455/697

Note: Tan ∝ = Sin ∝/Cos ∝

⇒ Tan (∝ + β) = (Sin ∝ + β)/(Cos ∝ + β)

Recall Sin (∝ + β) = 455/697 and Cos (∝ + β) = -528/697

∴ Tan (∝ + β) = (455/697)/(-528/697)

Tan (∝ + β) = 455 /697 x (-697/528)

Tan (∝ + β) = -455/528

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