Question

express the trigonometry ratios sin A,sec A,and tan A in terms of cot A​

Answer 1

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✏Express the trignometry ratios sin A, sec A, and tan A , in terms of cot A.

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➡Sin A , sec A, tan A, in term of cotA .

firstly ,

✏tan A = $\frac{1}{cot A}$

(1 + tan²= A = sec²= A)

➡Sec²A = 1 + tan² A

sec² A= 1 + $\frac{1}{cot A²}$

sec²A= $\frac{1}{1} + \frac{1}{cot²A}$

sec²A = $\frac{cot²A+1}{cot²A}$

sec²A= $\frac{\sqrt{cot²A+1}{cot²A}$

sec A= $\frac{\sqrt{cot²A+1}{cot+A}$

➡cosA =$\frac{cot + A}{\sqrt{cot²A+1}}$

sin²A = $\frac{1 + cot A²}{\sqrt{cot²A +1}}$

sin²A=$\frac{cot²A+1-cot²A}{cot²A+1}$

sin²A = $\frac{1}{cot²A+1}$

sinA=$\sqrt{\frac{1}{cot²A+1}}$

sinA=$\frac{1}{\sqrt{cot²+A+1}}$

➡sin²A + cos²A =1

Sin²A= 1-cos²A

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