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Grade 11Trigonometry

SecA – CosA =1,then tan²A/2=?

Abhinav Acharya

12 Years agoGrade 11

1 Answer

Jitender Singh

Approved Tutor Answer12 Years ago

Ans:

$secA-cosA = 1$

$\frac{1}{cosA}-cosA = 1$

$1-cos^{2}A = cosA$

$cos^{2}A+ cosA-1=0$

$cosA = \frac{-1\pm \sqrt{5}}{2}$

$cosA = \frac{-1+\sqrt{5}}{2}$

$cosA=1-2sin^{2}\frac{A}{2} = \frac{-1+\sqrt{5}}{2}$

$2-4sin^{2}\frac{A}{2} = \frac{-1+\sqrt{5}}{1}$

$4sin^{2}\frac{A}{2}=3-\sqrt{5}$

$sin^{2}\frac{A}{2}=\frac{3-\sqrt{5}}{4}$

$cos^{2}\frac{A}{2}=1-sin^{2}\frac{A}{2}=1-\frac{3-\sqrt{5}}{4}=\frac{1+\sqrt{5}}{4}$

$tan^{2}\frac{A}{2}=\frac{sin^{2}\frac{A}{2}}{cos^{2}\frac{A}{2}}=\frac{3-\sqrt{5}}{1+\sqrt{5}}$

Thanks & Regards

Jitender Singh

IIT Delhi

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