WebSep 30, 2016 · Since #cot theta=cos theta/sin theta and csc theta =1/sin theta#, the expression becomes: #(cos theta/sin theta)/(1/sintheta-sin theta)# that's #(cos theta/sin theta)/((1-sin^2 theta)/sin theta)#; then, since #1-sin^2 theta=cos^2 theta#, the expression becomes: #(cos theta/cancel sin theta)/(cos^2 theta/cancel sin theta)# WebMar 27, 2024 · Instead of using formulas, it'd be easier to solve it geometrically, with a right triangle. Since cscθ = 1 sinθ = hypotenuse opposite = c a = 4 3, this means that a and c are multiples of 3 and 4, respectively. In other words, we have c = 4k and a = 3k, for a real number k. By the Pythagorean theorem, b = √c2 − a2 = √16k2 − 9k2 = √7 ...
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WebFree trigonometric identity calculator - verify trigonometric identities step-by-step WebFeb 27, 2024 · cosec theta = 1/sin theta, sec theta = 1 / cos theta. (1/sin theta) / (1/cos theta) = cos theta/sin theta = 1/tan theta = cot theta. tan theta + cot theta = tan theta + 1/tan theta. Taking LCM, From the identities, 1 + tan^2 theta = sec^2 theta. = 1 / (sin theta*cos theta). This cannot be reduced, hence is equal to sec theta*cosec theta. philosophy\\u0027s r7
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WebConsider the diagram below. The terminal side of an angle \theta in standard position intersects the unit circle at the point (\cos\theta, \sin\theta). If \theta \neq \frac{\pi}{2} + n\pi, n \in \mathbb{Z} ... WebDec 20, 2024 · The Pythagorean identities are based on the properties of a right triangle. cos2θ + sin2θ = 1. 1 + cot2θ = csc2θ. 1 + tan2θ = sec2θ. The even-odd identities relate the value of a trigonometric function at a given angle to the value of the function at the opposite angle. tan( − θ) = − tanθ. WebFree math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. philosophy\u0027s r