Sep 21, 2015 · Simplify: csc^2 x - 1 Ans: cot^2 x 1/sin^2 x - 1 = (1 - sin^2 x)/sin^2 x = cos^2 x /sin^2 x = cot^2 x

Dec 13, 2015 · Prove 1 + cot^2 x = csc^2 x 1 + cot^2 x = 1 + cos^2 x/(sin^2 x) = (sin^2 x + cos^2 x)/(sin^2 x) = 1/(sin^2 x) = csc^2 x

May 5, 2016 · Left Side: #=csc^2theta+sec^2 theta# #=1/sin^2 theta + 1/cos^2 theta# #=(cos^2 theta + sin^2 theta)/(sin^2 theta cos^2 theta)#

Apr 13, 2018 · #csc^2(x)=1/sin^2(x)# #d/dx[csc^2(x)]=d/dx[1/sin^2(x)]# #d/dx[1/sin^2(x)]=d/dx[[sin(x)]^{-2}]# let #u=sinx#. #d/dx[[sin(x)]^{-2}]=d/{du}[u^{-2}]d/dx[sinx]#

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Aug 5, 2015 · How do you apply the fundamental identities to values of #theta# and show that they are true

Jan 3, 2018 · -1 One of the fundamental identities is 1+cot^2(x) = csc^2(x). Starting with your given: cot^2(x)-csc^2(x) Replace csc^2(x) with 1+cot^2(x): cot^2(x)-(1+cot^2(x)) =cot^2(x)-1 …

May 4, 2016 · see below Left Side:=csc^2 theta (1-cos^2 theta) = csc^2 theta * sin^2 theta = 1/sin^2 theta * sin^2 theta =1 = Right Side

Feb 23, 2017 · csc^2 x - 2csc - 2 = 0 Solve this quadratic equation for csc x. Since (a - b + c = 0), use shortcut. The 2 real roots are csc x = -1 and csc x = -c/a = 2 Convert csc = 1/(sin) to sin x, …

Mar 15, 2015 · The antiderivative of csc^2x is -cotx+C. Why? Before trying anything 'fancy' (subsitutuion, parts, trig sub, misc sub, partial fractions, et c.) try 'staightaway' …