Thursday

January 19, 2017
Posted by **yoshi** on Sunday, December 16, 2012 at 1:27pm.

= cos λ + sin λ

10. Prove that 1+tanθ/1-tanθ = sec^2θ+2tanθ/1-tan^2θ

17.Prove that sin^2w-cos^2w/tan w sin w + cos w tan w = cos w-cot w cos w

23. Find a counterexample to shows that the equation sec a – cos a = sin a sec a is not an identity.

- trignonmetry -
**Steve**, Sunday, December 16, 2012 at 3:37pmPLEASE tell your classmates to use parentheses to clarify the problems!

I think you mean

(tan*cos^2 + sin^2)/sin

= (sin*cos + sin^2)/sin

= sin(cos+sin)/sin

= cos+sin

I think you mean

(1+tan)/(1-tan)

= (1+tan)^2/(1-tan^2)

= (1+2tan+tan^2)/(1-tan^2)

= (sec^2+2tan)/(1-tan^2)

I think you mean

(sin^2 - cos^2)/(tan*sin+cos*tan)

= (sin-cos)(sin+cos)/(tan(sin+cos)

= (sin-cos)/tan

= sin*cot - cos*cot

= cos-cos*cot

always try simple values for counter-examples:

a=0: 1-1 =? 0 -- yes

a=pi: -1+1 =? 0 -- yes

a=pi/4: √2 - 1/√2 =? 1/√2*√2 NO!