query: Prove that type question of Trigonometric Identities
positive_passages.docid: 53135
positive_passages.text: Find $4\cos\theta-3\sin\theta$, given that $4\sin \theta +3\cos \theta = 5$
negative_passages.docid: 90226
negative_passages.text: Proving trigonometric equation $\cos(36^\circ) - \cos(72^\circ) = 1/2$
negative_passages.docid: 45619
negative_passages.text: Prove: $|a\sin x+b \cos x|\leq \sqrt{a^2+b^2}$
negative_passages.docid: 9986
negative_passages.text: Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $
negative_passages.docid: 13297
negative_passages.text: Prove the following trigonometric identity without a calculator involved
negative_passages.docid: 21088
negative_passages.text: Prove $\int\limits_{0}^{\pi/2}\frac{dx}{1+\sin^2{(\tan{x})}}=\frac{\pi}{2\sqrt{2}}\bigl(\frac{e^2+3-2\sqrt{2}}{e^2-3+2\sqrt{2}}\bigr)$
negative_passages.docid: 142835
negative_passages.text: Proving :$\arctan(1)+\arctan(2)+ \arctan(3)=\pi$
negative_passages.docid: 106355
negative_passages.text: How to prove Lagrange trigonometric identity
negative_passages.docid: 54175
negative_passages.text: Prove the trigonometric identity $\sin^4{x} = \frac{3-4\cos{2x}+\cos{4x}}{8}$
negative_passages.docid: 147005
negative_passages.text: Prove two identities relating to series
negative_passages.docid: 104384
negative_passages.text: Trigonometric identity: $\frac {\tan\theta}{1-\cot\theta}+\frac {\cot\theta}{1-\tan\theta} =1+\sec\theta\cdot\csc\theta$
negative_passages.docid: 123136
negative_passages.text: Proof of the identity: $c\sin \frac{A-B}{2} \equiv (a-b) \cos \frac{C}{2}$
negative_passages.docid: 21941
negative_passages.text: Proving: $x = a_0 + \sum_{n=1}^{\infty}(a_n \cos nx + b_n \sin nx)$
negative_passages.docid: 82758
negative_passages.text: To prove $ \tan(A) + 2 \tan(2A) +4\tan4A + 8 \cot8A =\cot(A) $
negative_passages.docid: 76490
negative_passages.text: Proving that $\cos(\arcsin(x))=\sqrt{1-x^2}$
negative_passages.docid: 145559
negative_passages.text: Trigonometry problem on product of trig functions.
negative_passages.docid: 143050
negative_passages.text: If $\tan(\frac{\pi}{4}+\frac{y}{2})=\tan^3(\frac{\pi}{4}+\frac{x}{2})$,then prove that $\sin y=\frac{\sin x(3+\sin^2 x)}{(1+3\sin^2 x)}$