sin x 4 2sin x 2 1 Trigonometry Examples Popular Problems Trigonometry Factor 1 2sin x 2 sin x 4 1 2sin2 x sin4 x 1 2 sin 2 x sin 4 x Factor using the perfect square rule Tap for more steps 1 sin2 x 2 1 sin 2 x 2 Rewrite 1 1 as 12 1 2 12 sin2 x 2 1 2
Explanation sin4x 2sin2x 1 sin2x 2 2 sin2x 1 12 sin2x 1 2 1 sin2x 2 cos2x 2 cos4x Answer link It is a perfect square sin 4 x 2sin 2 x 1 sin 2 x 1 2 Trigonometry is a branch of mathematics concerned with relationships between angles and side lengths of triangles In particular the trigonometric functions relate the angles of a right triangle with ratios of its side lengths
sin x 4 2sin x 2 1
sin x 4 2sin x 2 1
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Prove That Sin 2x 2sin x cos x Epsilonify
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Solve Sin 1 1 X 2 Sin 1 X Pi 2 Then X Is Trigonometry
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Free trigonometric identity calculator verify trigonometric identities step by step Popular Problems Precalculus Solve by Factoring 2sin x 2 sin x 1 2sin 2 x sin x 1 Subtract 1 from both sides of the equation 2sin2 x sin x 1 0 Let u sin x Substitute u for all occurrences of sin x 2u2 u 1 0 Factor by grouping Tap for more steps 2u 1 u 1 0 Replace all occurrences of u with sin x
Simplify frac sin 4 x cos 4 x sin 2 x cos 2 x simplify frac sec x sin 2 x 1 sec x sin x sin frac x 2 0 0 le x le 2 pi cos x sin x 0 3 tan 3 A tan A 0 A in left 0 360 right sin 75 cos 15 sin 120 csc frac 53 pi 6 prove tan 2 x sin 2 x tan 2 x sin 2 x prove cot 2x We just need to factor this This is a perfect square trinomial Since a2 2ab b2 a b 2 we can say a4 2a2 1 a2 1 2 Now switch back to the original situation Re substitute sinx for a sinx 4 2 sinx 2 1 cosx sinx 2 1 2 cosx sin2x 1 2 cosx We can now use a trigonometric identity to simplify the terms in blue
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Purplemath What is an identity In mathematics an identity is an equation which is always true regardless of the specific value of a given variable An identity can be trivially true such as the equation x x or an identity can be usefully true such as the Pythagorean Theorem s a2 b2 c2 MathHelp Need a custom math course Trigonometric identities like sin cos 1 can be used to rewrite expressions in a different more convenient way For example 1 sin cos can be rewritten as cos cos and then as cos
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sin x 4 2sin x 2 1 - Solve Evaluate 2x 1 x2 Differentiate w r t x 1 x22 1 2x2 Graph Quiz Trigonometry sin 2sin 1 x Similar Problems from Web Search Number of solutions to sin 1 x x 1 and friends math stackexchange q 1806572 The method of solution is pretty much the same for each of these