If x+y+z = 2pi , then prove that tan(x/2)tan(y/2)+tan(y/2)tan(z/2)+tan(z/2)tan(x/2)=1
If x+y+z = 2pi , then prove that tan(x/2)tan(y/2)+tan(y/2)tan(z/2)+tan(z/2)tan(x/2)=1
Loganayaki S , 6 Years ago
Grade 11
Trigonometry> If x+y+z = 2pi , then prove that tan(x/...
1 Answers
Arun
Last Activity: 6 Years ago
x+y+z=180
½x+½y+½z=90°
½x+½y=90-½z
② tan(½x+½y)=tan(90-½z)=cot½z=1/tan½z
(tan½x+tan½y)/(1-tan½xtan½y) =1/tan½z
tan½z(tan½x+tan½y)=1-tan½xtan½y
∴ tan½xtan½z+tan½ztan½y+tan½xtan½y=1
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