cos^2x-sin^2x= -cosx# #cos 2x= cos (- x)# #=> 2x = -x => 3x = 0 ,x = 0# Right this is a definite solution. Lets go back to the equation #2cos^2 x - 1 = - cos x# Bring everything over to one side. Let # cos x = a# #2a^2 + a -1 = 0# Factoring you get #(2a -1)(a + 1) = 0# #2a - 1 = 0# #a = 1/2# Solvethe Following Equation: Cosx + Sin X = Cos 2x + Sin 2x . Department of Pre-University Education, Karnataka PUC Karnataka Science Class 11. Textbook Solutions 10542. Important Solutions 3. Question Bank Solutions 5825. Concept Notes & Videos 688 Syllabus. Advertisement Remove क्रमाक्रमानेसोल्यूशनसह आमचे विनामूल्य गणित सॉलव्हर वापरून Freemath problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Solveyour math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. Applytrig identity: #cos 2x = 1 - 2sin^2 x# #sin x = 1 - 2sin^2 x#. Solve the quadratic equation: #2sin^2 x + sin x - 1 = 0# Since (a - b + c = 0), use Shortcut. Two real roots: sin x = -1 and #sin x = -c/a = 1/2#. #sin x = 1/2#--> x = 30 deg and x = 150 deg #(pi/6 and (5pi)/6)# sin x = -1 --> x = 270 deg #((3pi)/2)# General solutions: x = 30 Takingsquare root on both sides. cosx + sinx = sinx ± √1 - sin 2 x. By using the cofunction or complement identity. cosx = sin (π/2 - x) sinx + cosx = sinx + sin (π/2 - x) Therefore, when asked What is sin x + cos x in terms of sine? then the answer will be sin x + cos x in terms of sine is sinx + sin (π/2 - x). tanx y) = (tan x tan y) / (1 tan x tan y) . sin(2x) = 2 sin x cos x cos(2x) = cos ^2 (x) - sin ^2 (x) = 2 cos ^2 (x) - 1 = 1 - 2 sin ^2 (x) . tan(2x) = 2 tan(x) / (1 4mxsz. cosxsinx = sin2x/2 Explanation So we have cosxsinx If we multiply it by two we have 2cosxsinx Which we can say it's a sum cosxsinx+sinxcosx Which is the double angle formula of the sine cosxsinx+sinxcosx=sin2x But since we multiplied by 2 early on to get to that, we need to divide by two to make the equality, so cosxsinx = sin2x/2

cos x sin x cos 2x