Prove the trigonometric identity tan^2(x)+1=sec^2(x)
We can start with the identity sin2(x)+cos2(x)=1 If we divide through the equation by cos2(x), we get: sin2(x)/cos2(x) + cos2(x)/cos2(x) = 1/cos2(x) If we look at the left hand side of the equation: sin2(x)/cos2(x) is equal to tan2(x), and cos2(x)/cos2(x) is equal to 1 (as it is divided through by itself), the left hand side becomes tan2(x) +1 Now if we look at the right hand side of the equation: 1/cos2(x) is equal to sec2(x) Putting both sides of the equation together, we get tan2(x) +1=sec2(x)
CW
Related Maths A Level answers
All answers ▸A curve has equation y = 2x^5 + 5x^4 1 . (a) Find: (i) dy/ dx [2 marks] (ii) d^2y/ dx^2 (b) The point on the curve where x ¼ 1 is P. (i) Determine whether y is increasing or decreasing at P, giving a reason for your answer.
I don't understand the point of differentiation or integration
∫ (ln(x)/(x*(1+ln(x))^2) dx
Differentiate with respect to x: y = ln(x^2+4*x+2).