sec(θ) = 1 / cos(θ) 由此,我们可以推导出它们之间的转化关系: tan(θ) = sin(θ) * sec(θ)(因为 sec(θ) = 1 / cos(θ)) 在知道 tan(θ) 的情况下,sec(θ) = √(1 + tan²(θ))(利用 Pythagorean identity:sin²(θ) + cos²(θ) = 1,以及 tan(θ) = sin(θ) / cos...
Answer to: Prove the following identity. sec (x) csc (x) - cot (x) = tan (x) By signing up, you'll get thousands of step-by-step solutions to your...
The given trigonometric identity is {eq}\dfrac{\tan \left(\theta \right) + \sec \left(\theta \right) - 1}{ \tan \left(\theta \right)-\sec \left(\theta... Learn more about this topic: Pythagorean Identity Theorem | Definition, Formula & E...
解析 Simplify by multiplying through.( ((sec))^2(x)-((tan))^2(x)+((csc))^2(x)-((cot))^2(x))Apply pythagorean identity.( 1+((csc))^2(x)-((cot))^2(x))Apply pythagorean identity.( 1+1)Add ( 1) and ( 1).( 2)...
( (((sec))^2(x)-((tan))^2(x))/(((cot))^2(x)-((csc))^2(x))) 相关知识点: 试题来源: 解析 Apply pythagorean identity. ( 1/(((cot))^2(x)-((csc))^2(x))) Simplify with factoring out. ( 1/(-(((csc))^2(x)-((cot))^2(x))) Apply pythagorean ide...
Apply pythagoreanidentity. sec2(x)sec2(x) Because the two sides have been shown to beequivalent, theequationis anidentity. tan2(x)+1=sec2(x)tan2(x)+1=sec2(x)is anidentity tan2(x)+1=sec2(x)tan2(x)+1=sec2(x)
Step 1: Use the Pythagorean IdentityWe know from trigonometric identities that:sec2θ−tan2θ=1This can be rearranged to express sec2θ:sec2θ=1+tan2θ Step 2: Substitute sec2θ in the ExpressionNow, substitute sec2θ in the original expression:sec2θ−1tan2θ=(1+tan2θ)−1tan...
We know from the Pythagorean identity that:sec2θ=1+tan2θUsing this identity, we can simplify sec2θ−tan2θ:sec2θ−tan2θ=(1+tan2θ)−tan2θ=1 Step 4: Substitute back into the factored expressionNow substitute this back into our factored expression:sec4θ−tan4θ=(1)(sec2...
tan^2x- cot ^2x= sec ^2x- csc^2 x 相关知识点: 试题来源: 解析 Common denominator. Simplify using Pythagorean identity.If you don't know how it works, please review Fundamental Trigonometry Identities (Section 7.1) and Special Product Formulas (Section 1.3). LHS=((sin )^2x)((cos )^...
-(sec2(x)-tan2(x)) -(sec2(x)-tan2(x)) −(sec2(x)−tan2(x))-(sec2(x)-tan2(x)) Apply pythagoreanidentity. −1⋅1-1⋅1 Multiply−1-1by11. −1-1 (tan(x)+sec(x))(tan(x)−sec(x))(tan(x)+sec(x))(tan(x)-sec(x)) ...