SOLUTION: establish the identity.
sin(θ+β)/tan(α)tan(β)= cos(α)cos(β)
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Question 799186: establish the identity.
sin(θ+β)/tan(α)tan(β)= cos(α)cos(β)
Answer by harpazo(655) (Show Source): You can put this solution on YOUR website!
Use the following trig identities:
sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
tan(A) = sin(A)/cos(A)
tan(B) = sin(B)/cos(B)
Substitute the above into your equation and simplify the left side to look like the right side.
sin (A + B) = (sin A)(cos B) + (cos A)(sin B) ; Divide both sides by (cos A)(cos B)
=> sin (A + B) / {(cos A)(cos B)} = (sin A)/(cos A) + (sin B)/(cos B)
=> sin (A + B) / {(cos A)(cos B)} = tan A + tan B
=> sin (A + B) / (tan A + tan B) = (cos A)(cos B)
Verify your question.
Question for you:
Is the denominator of LHS (tan A) + tan B) or (tan A)(tan B)? You did not make this clear in your post.
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