We are learning trig identities in my pre-calc class, and I am working on a homework assignment. I can work out every problem except this one. Could someone please help? We have to make the left side of the equation match the right side. For example:
(1 + sinx)(1 - sinx) = cos^2x
(1 - sin^2x) = cos^2x
cos^2x = cos^2x
The equation that I cannot solve is:
(tanx + cosx)/tanx = csc^2x
**We are allowed to use reciprocal identities, quotient identities, and pythagorean identities.
(1 + sinx)(1 - sinx) = cos^2x
(1 - sin^2x) = cos^2x
cos^2x = cos^2x
The equation that I cannot solve is:
(tanx + cosx)/tanx = csc^2x
**We are allowed to use reciprocal identities, quotient identities, and pythagorean identities.
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This is not an identity. For example, when x = π/4,
(tanx + cosx)/tanx = (1 + 1/√2)/1 = 1 + 1/√2, but
csc²(π/4) = 1/sin²(π/4) = 1/½ = 2.
Is there a typo?
(tanx + cosx)/tanx = (1 + 1/√2)/1 = 1 + 1/√2, but
csc²(π/4) = 1/sin²(π/4) = 1/½ = 2.
Is there a typo?