SOLUTION: Hi. Please help me prove that this equation is an identity because I really don't know what to do. Thank you!
(cot B / sec B - tan B) - (cos B / sec B + tan B) = sin B + csc
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-> SOLUTION: Hi. Please help me prove that this equation is an identity because I really don't know what to do. Thank you!
(cot B / sec B - tan B) - (cos B / sec B + tan B) = sin B + csc
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Question 602392: Hi. Please help me prove that this equation is an identity because I really don't know what to do. Thank you!
(cot B / sec B - tan B) - (cos B / sec B + tan B) = sin B + csc B Answer by solver91311(24713) (Show Source):
The LCD in the LHS is the product of the two denominators. The two denominators are a conjugate pair, hence the product is the difference of two squares. Apply the LCD:
Use the fact that tangent is sine over cosine, cotangent is the reciprocal of tangent, secant is the reciprocal of cosine, and cosecant is the reciprocal of sine to write:
Simplify the LHS numerator:
Combine the fractions in the LHS denominator:
Use the Pythagorean identity in the LHS denominator:
Finally, apply cosecant is the reciprocal of sine
John
My calculator said it, I believe it, that settles it
