Howdo(tanx-1)(sin2x-2cos²x)= 2(1-2sinxcosx)
0
0
1 Isticmaale1 Answer
You must login to add an answer.
caawiye app Latest Questions
1 Isticmaale1 Isticmaale1 IsticmaaleREGISTER! Share and grow knowledge of the world! We want to connect educated people with those who need it, to bring them together and to be able to share their knowledge with everyone. Join the Questions & Answers here.
Please sign in to your account!
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
1 IsticmaaleYou must login to add an answer.
We can start by using the trigonometric identity:
sin(2x) = 2sin(x)cos(x)
We can substitute this identity into the expression:
(tan(x) – 1)(sin(2x) – 2cos²(x))
= (tan(x) – 1)(2sin(x)cos(x) – 2cos²(x)) (substituting sin(2x) with 2sin(x)cos(x))
= -2cos(x)(tan(x) – 1)(cos(x) – sin(x)) (factoring out a -2cos(x) from the second term)
= -2cos(x)(sin(x) – cos(x))(tan(x) – 1)(-1) (multiplying the second term by -1 and rearranging)
= 2cos(x)(cos(x) – sin(x))(1 – tan(x))
= 2cos(x)(cos(x) – sin(x))(1 – sin(x)/cos(x)) (substituting tan(x) with sin(x)/cos(x))
= 2(cos(x) – sin(x))(cos(x)/cos(x) – sin(x)/cos(x))
= 2(cos(x) – sin(x))(1 – sin(x)cos(x)/(cos(x))^2)
= 2(cos(x) – sin(x))(1 – sin(x)cos(x))
= 2(cos(x) – sin(x) + sin(x)cos(x) – sin(x)²cos(x))
= 2(1 – sin(x)cos(x) – 2sin(x)cos(x))
= 2(1 – 3sin(x)cos(x))
= 2(1 – 2sin(x)cos(x) – sin(x)cos(x))
= 2(1 – 2sin(x)cos(x)) (since sin(x)cos(x) = 1/2 sin(2x))
Therefore, (tan(x) – 1)(sin(2x) – 2cos²(x)) = 2(1 – 2sin(x)cos(x)) as required.