WebExpert Answer. Solve the problem. For what numbers theta is f (theta) = cot theta not defined? odd multiples of pi (180 degree) all real numbers integral multiples of pi (180 degree) odd multiples of pi/2 (90 degree) Solve the problem. What is the range of the cosine function? all real numbers greater than or equal to 1 or less than or equal to ... WebAug 21, 2016 · Explanation: Since cscθ = 1 sinθ and cotθ = cosθ sinθ, you can substitute and have: (cscθ − cotθ)2 = ( 1 sinθ − cosθ sinθ)2. = ( 1 −cosθ sinθ)2 = (1 −cosθ)2 sin2θ. Since sin2θ = 1 − cos2θ, the expression becomes: = (1 −cosθ)2 1 −cos2θ = (1 −cosθ)2 (1 − cosθ)(1 + cosθ) = 1 −cosθ 1 +cosθ.
Solved ify the identity tan(θ)cos(θ)sec(θ)=cot(θ) uestion 2 - Chegg
WebDec 10, 2024 · If tanθ = cotθ = a and sinθ + cos θ = b, then solve (b^2 - 1)^2(a^2 + 4). asked Dec 7, 2024 in Trigonometry by RiteshBharti ( 54.1k points) trigonometric identities Webcot (θ) = −1 cot ( θ) = - 1. Take the inverse cotangent of both sides of the equation to extract θ θ from inside the cotangent. θ = arccot(−1) θ = arccot ( - 1) Simplify the right side. Tap for more steps... θ = 3π 4 θ = 3 π 4. The cotangent function is negative in the second and fourth quadrants. To find the second solution ... bob hershey nasa
How do you simplify (1+costheta)(csctheta-cottheta)? Socratic
WebAug 1, 2024 · #(1 + tan theta) / (1 + cot theta)# #=> (1 + sin theta/cos theta) / (1 + cos theta / sin theta)# #=> (cancel(cos theta + sin theta)/cos theta) / (cancel(sin theta ... WebJan 17, 2024 · We have a common denominator in the second factor, so let's write it as a single quotient. = (1 +cosθ) (1 − cosθ) sinθ. Now watch and pay attention. This is a good trick to know. = (1 +cosθ)(1 − cosθ) sinθ. = 1 − cos2θ sinθ. And we can simplify some more, = sin2θ sinθ. = sinθ. WebI have to prove the following result : $$\\frac {\\tan\\theta}{1-\\cot\\theta}+\\frac {\\cot\\theta}{1-\\tan\\theta} =1+\\sec\\theta\\cdot\\csc\\theta$$ I tried ... clip art lily flower