Math Is Fun Forum

jcd29

Member

Registered: 2008-01-24

Posts: 1

trigonometric identities..help!!

there's a few problems that I can't solve..maybe you guys can help me:

1)    [sin(x-y)] / [cos(x+y)] = [tan(x)-tan(y)] / [1-tan(x)tan(y)]

2) [cot^2(u)-1] / [cot^2(u)+1] = [csc^2(u)-sec^2(u)] / [csc^2(u)+sec^2(u)]

3) [sec^2(u)-tan^2(u)+tan(u)] / sec(u) = sin(u)+cos(u)

It's really urgent..my brother has a test tomorrow and I'm trying to help him, so knowing how to solve this would help a lot. Thanks.

saudi_boy

Member

Registered: 2006-11-01

Posts: 41

Re: trigonometric identities..help!!

1.  [sin(x-y)] / [cos(x+y)] = [tan(x)-tan(y)] / [1-tan(x)tan(y)]

Left side

now divide {numerator}{denominator} by cos(y)cos(x)

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: trigonometric identities..help!!

3) [sec^2(u)-tan^2(u)+tan(u)] / sec(u) = sin(u)+cos(u)

3) [sec^2(u)-tan^2(u)+tan(u)] / sec(u)
= [1 + tan(u)] / sec(u)
= cos(u) + sin(u)
= sin(u) + cos(u)

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