Step 1: Use the identity for sin3θWe know that:sin3θ=3sinθ−4sin3θSubstituting this into the equation gives:3sinθ−4sin3θ=4sinθ(sin2x−sin2θ) Step 2: Expand the right-hand sideExpanding the right-hand side:3sinθ−4sin3θ=4sinθsin2x−4sinθsin2θ Step 3: Rea...
If the terms on both sides are equal, then the identity is true. Answer and Explanation: Become a Study.com member to unlock this answer! Create your account View this answer Given: $$\sin \theta \csc^{2} \theta= \csc \theta $$ Our objective is to prove the given id...
Verify the trigonometric identity: {eq}\displaystyle \sin \theta \tan \theta + \cos \theta = \sec \theta {/eq}. Trigonometric Identities: Trigonometric identities are equality functions that are true for any value of the unknown angle quantity. For example, {eq}\cos 2x ...
{eq}\displaystyle \dfrac {\sec^2 \theta - 1} {\sec^2 \theta} = \sin^2 \theta {/eq} Verifying the Trigonometric Identity: To verify the trigonometric identity, try to reduce or simplify the one side of the equation till we get the same expression as the other side of the ...
( (1+(sin)(θ )+(cos)(θ ))/(1+(sin)(θ )-(cos)(θ ))=(1+(cos)(θ ))/((sin)(θ ))) 相关知识点: 试题来源: 解析 The provided equation is an identity but there are no steps available. ( (1+(sin)(θ )+(cos)(θ ))/(1+(sin)(θ )-(cos)(θ ))=(1+(cos)(...
Half-angle formula for sine function: {eq}\sin 2\theta=2\sin \theta\cos \theta {/eq} Answer and Explanation:1 We are given a trigonometric expression. We want to prove that it is an identity. Using the identities on the context section we have that: ...
sin3θ=(sinAcosθ−cosAsinθ)(sinBcosθ−cosBsinθ)(sinCcosθ−cosCsinθ) Step 4: Expand the right-hand sideExpanding the right-hand side will yield a more complex expression. However, we can use the identity A+B+C=π to simplify our calculations later. Step 5: Analyze the ...
sin2(θ2)=secθ-12secθ Use the appropriate power-reducing formula and rewrite the left side of the identity. 1-cosθ (Simplify your answer.) Rewrite the expression from the previous step by multiplying the numerator and denominator by secθ...
We use a trigonometric identity and elementary calculus to obtain simple proofs of the following identities: csc~2θ=1/θ~2+∞∑(k=1) (1/(kπ+θ)~2 +1/(kπ-θ)~2), cotθ=1/θ - ∞∑(k=1) 2θ/(k~2π~2-θ~2) and sinθ=θ ∞∏(k=1) (1-θ~2/(k~2π~2)).关键...
https://math.stackexchange.com/questions/1525591/graphical-interpretation-of-the-trigonometric-identity-a-cos-thetab-sin-the The basic intuition that I apply to this question is that we are dealing here with various sinusoidal functions with period 2π. The functio...