Question

1 Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.
2. Write all the other trigonometric ratios of ZA in terms of sec A.
3. Evaluate​

Answer 1

And : first we take one right angled triangle∆ A,B,C ..... in which 90 degree at angle B .

so sin A = p/h = BC/ AC ,

Let BC = x and AB = x cot A

Now, ln ∆ ABC , ( we have to use Pythagoras theorem to find hypotenuse side )

p²+ b²=h²

x²+(x cot A )²=H²

x²+x²cot²A=H²

√x²+x²cot²A=H

√x²(1+cot²A)=H

x√1+cot²A=H

so,

we find our (hypotenuse side) also ,

Sin A= p/h=x/x(1+cot²A)=1/1+cot²A

sec A=h/b=x (1+cot²A) /x cot A =1+cot²A/ cotA

tan A = P/b = x /x cot A = 1/cot A

finish ....

I hope it helps u