ok shall we try this i will pass step by step and clarify Given: a million. a million/+sinx + a million/a million-sinx = 2sec^2x 2. a million(a million-sinx)/(a million+sinx)(a million-sinx) + a million(a million+sinx)/(a million-sinx)(a million+sinx) On step 2 I prolonged a million/(a million+sinx) by (a million-sinx) to the numerator and the denominator Then the second one portion of the left hand side, I prolonged a million/(a million-sinx) by (a million+sinx) to the numerator and denominator This makes both numbers have a similar denominator so that you'll combine them 3. (a million-sinx)/a million-sin^2x + (a million+sinx)/a million-sin^2x in the experience that your questioning about the denominator (a million+sinx)(a million-sinx) = a million-sin^2x because shall we assume of of it like algebra (x+y)(x-y) = x^2 - y^2 4. (a million-sinx) + (a million+sinx) / (cos^2x) All i did in this step became combine both numbers because they have a similar denominator and altered a million-sin^2x to cos^2x (pythagorean theorem) 5. 2/cos^2x 6. 2 x a million/cos^2x this step is fairly puzzling. i split the equation up into 2 aspects because if u multiply 2 by a million/cos^2x thats basically 2/cos^2x its like splitting 3/2 into 3 x a million/2 7. 2 x sec^2x Rule : a million/cos = sec and because u have a million/cos^2 thats basically sec^2 8. 2sec^2x there you only proved it . desire it wasn't to lengthy and hopefully you understood this
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TRIGONOMETRY FORMULAS TO BE USED.
# 1+cos 2x= 2 cos^2x .....(1)
# sin2x= 2sinx cosx ......(2)
LHS
(1+cos2x)/sin2x
2cos^2x/ 2sinx cosx .....[from (1) &(2)]
cosx/sinx
cotx=RHS
Hence, proved.
Hope it helps!
ok shall we try this
i will pass step by step and clarify Given: a million. a million/+sinx + a million/a million-sinx = 2sec^2x 2. a million(a million-sinx)/(a million+sinx)(a million-sinx) + a million(a million+sinx)/(a million-sinx)(a million+sinx) On step 2 I prolonged a million/(a million+sinx) by (a million-sinx) to the numerator and the denominator Then the second one portion of the left hand side, I prolonged a million/(a million-sinx) by (a million+sinx) to the numerator and denominator This makes both numbers have a similar denominator so that you'll combine them 3. (a million-sinx)/a million-sin^2x + (a million+sinx)/a million-sin^2x in the experience that your questioning about the denominator (a million+sinx)(a million-sinx) = a million-sin^2x because shall we assume of of it like algebra (x+y)(x-y) = x^2 - y^2 4. (a million-sinx) + (a million+sinx) / (cos^2x) All i did in this step became combine both numbers because they have a similar denominator and altered a million-sin^2x to cos^2x (pythagorean theorem) 5. 2/cos^2x 6. 2 x a million/cos^2x this step is fairly puzzling. i split the equation up into 2 aspects because if u multiply 2 by a million/cos^2x thats basically 2/cos^2x its like splitting 3/2 into 3 x a million/2 7. 2 x sec^2x Rule : a million/cos = sec and because u have a million/cos^2 thats basically sec^2 8. 2sec^2x there you only proved it 
. desire it wasn't to lengthy and hopefully you understood this
cos 2x = cos^2 x - sin^2 x
1 = cos^2 x + sin ^2 x
sin 2x = 2sin x cos x
So, on substituting, we get cos x / sin x = cot x
(1+cos2x)/sin2x
(1+(2(cosx)^2-1)/sin2x
2(cosx)^2/sin2x
2(cosx)^2/2sinx cosx
cosx/sinx
cotx
(1 + cos(2x)) / sin(2x)
= (1 + 2cos²(x) - 1) / (2 sin(x) cos(x))
= 2 cos²(x) / (2 sin(x) cos(x))
= cos(x) / sin(x)
= cot(x)
cos(2x) = 2cos²(x) - 1
sin(2x) = 2sin(x)cos(x)
(1 + 2cos²(x) - 1)/(2sin(x)cos(x)) = cos²(x)/(sin(x)cos(x)) = cos(x)/sin(x) = cot(x)