(sin(x)+cos(x))2 = 1+ 2sin(x)cos(x) ( sin ( x) + cos ( x)) 2 = 1 + 2 sin ( x) cos ( x) is an identity. Thus, sin(x)cos(x) = sin(2x) 2. Csc (theta) = 1 / sin (theta) = c / a. ( math | trig | identities) sin (theta) = a / c. Often, if the argument is simple enough, the function value will be written without parentheses, as sin θ rather than as sin(θ). Each of sine and cosine is a function of an angle, which is usually expressed in terms of radians or degrees.except where explicitly. Suppose that sinx + cosx = rsin(x + α) then sinx + cosx = rsinxcosα + rcosxsinα = (rcosα)sinx + (rsinα)cosx the coefficients of sinx and of cosx must be equal so rcosα = 1 rsinα = 1 squaring and adding, we get r2cos2α +r2sin2α = 2 so r2(cos2α +sin2α) = 2 r = √2 and now cosα = 1 √2 sinα = 1 √2 so α = cos−1( 1 √2) = π 4 Tan (theta) = sin (theta) / cos (theta) = a / b. Cos θ = 1/sec θ or sec θ = 1/cos θ; Sin θ = 1/csc θ or csc θ = 1/sin θ;
Tan (theta) = sin (theta) / cos (theta) = a / b. Web the reciprocal trigonometric identities are: Sec (theta) = 1 / cos (theta) = c / b. (sin(x)+cos(x))2 = 1+ 2sin(x)cos(x) ( sin ( x) + cos ( x)) 2 = 1 + 2 sin ( x) cos ( x) is an identity. Cos θ = 1/sec θ or sec θ = 1/cos θ; Tan θ = 1/cot θ or cot θ = 1/tan θ; Web we will use the identity sin(2x) = 2sin(x)cos(x). Sin(x)cot(x) = cos(x) sin ( x) cot ( x) = cos ( x) is an identity Cos (theta) = b / c. Suppose that sinx + cosx = rsin(x + α) then sinx + cosx = rsinxcosα + rcosxsinα = (rcosα)sinx + (rsinα)cosx the coefficients of sinx and of cosx must be equal so rcosα = 1 rsinα = 1 squaring and adding, we get r2cos2α +r2sin2α = 2 so r2(cos2α +sin2α) = 2 r = √2 and now cosα = 1 √2 sinα = 1 √2 so α = cos−1( 1 √2) = π 4 Web 1+2sin(x)cos(x) 1 + 2 sin ( x) cos ( x) because the two sides have been shown to be equivalent, the equation is an identity.
