Answers: 1
![\bf [cot(\theta )+csc(\theta )]^2=\cfrac{1+cos(\theta )}{1-cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the left-hand side}}{[cot(\theta )+csc(\theta )]^2}\implies cot^2(\theta )+2cot(\theta )csc(\theta )+csc^2(\theta ) \\\\\\ \cfrac{cos^2(\theta )}{sin^2(\theta )}+2\cdot \cfrac{cos(\theta )}{sin(\theta )}\cdot \cfrac{1}{sin(\theta )}+\cfrac{1}{sin^2(\theta )}\implies \cfrac{cos^2(\theta )}{sin^2(\theta )}+\cfrac{2cos(\theta )}{sin^2(\theta )}+\cfrac{1}{sin^2(\theta )}](/tpl/images/0002/3675/3a2cc.png)
![\bf \cfrac{\stackrel{\textit{perfect square trinomial}}{cos^2(\theta )+2cos(\theta )+1}}{sin^2(\theta )}\implies \boxed{\cfrac{[cos(\theta )+1]^2}{sin^2(\theta )}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the right-hand-side}}{\cfrac{1+cos(\theta )}{1-cos(\theta )}}\implies \stackrel{\textit{multiplying by the denominator's conjugate}}{\cfrac{1+cos(\theta )}{1-cos(\theta )}\cdot \cfrac{1+cos(\theta )}{1+cos(\theta )}}](/tpl/images/0002/3675/10f6e.png)
![\bf \cfrac{[1+cos(\theta )]^2}{\underset{\textit{difference of squares}}{[1-cos(\theta )][1+cos(\theta )]}}\implies \cfrac{[cos(\theta )+1]^2}{1^2-cos^2(\theta )} \\\\\\ \cfrac{[cos(\theta )+1]^2}{1-cos^2(\theta )}\implies \boxed{\cfrac{[cos(\theta )+1]^2}{sin^2(\theta )}}](/tpl/images/0002/3675/32d47.png)
Another question on Mathematics
Mathematics, 21.06.2019 18:30
If, while training for a marathon, you ran 60 miles in 2/3 months, how many miles did you run each month? (assume you ran the same amount each month) write your answer as a whole number, proper fraction, or mixed number in simplest form. you ran __ miles each month.
Answers: 1
Mathematics, 21.06.2019 19:00
Eis the midpoint of line segment ac and bd also line segment ed is congruent to ec prove that line segment ae is congruent to line segment be
Answers: 3
Mathematics, 21.06.2019 20:00
Which fraction is equal to 1hole and 2/5? a.3/5 b.75 c.57 d.73
Answers: 2
You know the right answer?
Prove the following(cot0+cosec0)[tex](cot0 + cosec0) { }^{2} = \frac{1 + cos0}{1 - cos0} [/tex]...
Questions
Mathematics, 13.11.2020 22:00
English, 13.11.2020 22:00
Mathematics, 13.11.2020 22:00
SAT, 13.11.2020 22:00
History, 13.11.2020 22:00
Mathematics, 13.11.2020 22:00
Mathematics, 13.11.2020 22:00
Mathematics, 13.11.2020 22:00
Mathematics, 13.11.2020 22:00
Mathematics, 13.11.2020 22:00
