Posted by yoshi on .
6. Prove that tan λ cos^2 λ + sin^2λ/sin λ
= cos λ + sin λ
10. Prove that 1+tanθ/1tanθ = sec^2θ+2tanθ/1tan^2θ
17.Prove that sin^2wcos^2w/tan w sin w + cos w tan w = cos wcot 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,
PLEASE 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)/(1tan)
= (1+tan)^2/(1tan^2)
= (1+2tan+tan^2)/(1tan^2)
= (sec^2+2tan)/(1tan^2)
I think you mean
(sin^2  cos^2)/(tan*sin+cos*tan)
= (sincos)(sin+cos)/(tan(sin+cos)
= (sincos)/tan
= sin*cot  cos*cot
= coscos*cot
always try simple values for counterexamples:
a=0: 11 =? 0  yes
a=pi: 1+1 =? 0  yes
a=pi/4: √2  1/√2 =? 1/√2*√2 NO!