1) 1+cos(3t)/ sin(3t) + sin(3t)/( 1+ cos(3t))= 2csc(3t) 2) sec^2 2u-1/ sec^2 2u= sin^2 2u 3) cosB/1- sinB= secB+ tanB
How would you establish this identity: (1+sec(beta))/(sec(beta))=(sin^2(beta))/(1-cos(beta))on the right, sin^2 = 1-cos^2, that factor to 1-cos * `1+cos, then the denominator makes the entire right side 1+cosB which is 1+1/sec which is 1/sec (sec+1) qedusing sec(beta) = 1/cos(beta): 1+sec(beta))/(sec(beta))= 1 + cos(beta) sin^2(beta)/(1-cos(beta)) = (1-cos^2(beta))/(1-cos(beta)) = 1 + cos(beta) This follows e.g. from: (1 - x^2) = (1 - x)(1 + x) and thus: (1 - x^2)/(1 - x) = 1 + x
find all solutions in the interval [0,2 pi) sin(x+(3.14/3) + sin(x- 3.14/3) =1 sin^4 x cos^2 xSince sin (a+b) = sina cosb + cosb sina and sin (a-b) = sina cosb - cosb sina, the first problem can be written 2 sin x cos (pi/3)= sin x The solution to sin x = 1 is x = pi/2 For your other problem sin^4 cos^2 x = sin^4 x(1 - sin^2x)=0 The solutions are sin x = 0 and sin^2 x...
Given: SinA=4/5 cosA=3/5 sinB=-5/13 cosB=-12/13 tanA=4/3 tanB=-5/-12cos(A-B)=?csc(A-B)=?sec(2B)=?tan(B/2)=?cos(B/2)=?Exact answers, no decimals.
show that (1+tanA tanB)^2 +(tanA -tanB)^2 =secA^2 secB^2
If a and B are two angles in Quadrant 2 such that tan a=-1/2 and tan B= -2/3, find cos(a+b)?tan(a) = -1/2oppsite side = 1: adjacentside = 2hypotenuse = sqrt(1+4) = sqrt(5)sin(a) = 1/併5cos(a) = -2/併5tan(b) = -2/3opposite side = 2 and adjacentside = 3hypotenuse = sqrt(4+9) = 併13sin(b) = 2/併13cos(b) = -3/併13cos(a+b) = cosa cosb - sina sinb=(-2/併5)(-3/併13) - (1/併5)(2/併13)= 6/併65 - 2/併65= 4/併65right?
verify that each of the following is an identity: 1) cos x/ 1-sin^2x= sec x 2) sec x/sin x - sin x/cos x = cot x 3) 1+tan^2ø/ cos ^2ø = sec^4 ø I really need ur help :) thank u so much
prove these identiessin^2+tan^2=sec^2-cos^2 sin^2 sec^2 +sin^2=tan^2+sin^2
If cos A = 1/3 with 0 < A< pi/2, and sinB=1/4, with pi/2<B<pi. calculate cos(A+B).My answer is (-sqrt15-2sqrt2)/12But the back of the book says the answer is (-sqrt15+2sqrt2)/12Am I wrong or the back? Please explain
verify those 3 identitiscsc x- cos x cot x = sin xsec 2x= sec^2x/2-sec^2xsin4x-sin3x/cos4x+ cos3x= 1-cos x/sinx
for (sec x -1)(sec x + 1) = tan^(2) x so far I got up to: (sin^(2)x / cos x) (-sin^(2)x / cos x) what would the next step be? steps too please
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