The correct option is B. p 2-1 2 p. Explanation for the correct option: Step 1: Given information . sec θ + tan θ = p. 1. Step 2: Simplification and calculate the value of tan θ. We know that the trigonometrical ratio formula . sec 2 θ-tan 2 θ = 1 ⇒ sec θ + tan θ sec θ-tan θ = 1 ∵ a 2-b 2 = a + b a-b. Put the value of sec θ tan (A –B) = [(tan A – tan B)/(1 + tan A tan B)] If none of the angles A, B and (A ± B) is a multiple of π, then cot (A + B) = [(cot A cot B − 1)/(cot B + cot A)] cot (A – B) = [(cot A cot B + 1)/(cot B – cot A)] Some additional formulas for sum and product of angles: cos (A + B) cos (A – B) = cos2A – sin2B = cos2B– sin2A To calculate the sine of a half angle sin (x/2), follow these short steps: Write down the angle x and replace it within the sine of half angle formula: sin (x/2) = ± √ [ (1 - cos x)/2]. Determine the sign using the half angle: Positive (+) if the half angle lies on the 1st or 2nd quadrants; or. I have these from textbooks: $\sin2\theta = 2\sin\theta \cos\theta$ $\cos2\theta = \cos^2\theta - \sin^2\theta$ $\tan2\theta = \dfrac{2\tan\theta}{1-\tan^2\theta} $ I d Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn To show you where the first of the double-angle identities for cosine comes from, this example uses the angle-sum identity for cosine. Because the two angles are equal, you can replace β with α, so cos (α + β) = cosα cosβ – sin sinβ becomes. To get the second version, use the first Pythagorean identity, sin 2 + cos 2 = 1. Write the double-angle formula for tangent. \(\tan(2\theta)=\dfrac{2 \tan \theta}{1−{\tan}^2\theta}\) In this formula, we need the tangent, which we were given as \(\tan \theta=−\dfrac{3}{4}\). Substitute this value into the equation, and simplify. Solution. In ΔABC by sine rule, we have. a A = b B = c C = k. a=ksinA,b=ksinB and c=ksinC. Now, consider. a - b a + b = k A - k B A + B. = sin A - sin B sin A + sin B. = 2 cos ( A + B 2). sin ( A - B 2) 2 sin ( A + B 2). cos ( A - B 2) = cot ( A + B 2). tan ( A - B 2) tan(x y) = (tan x tan y) / (1 tan x tan y). sen(2x) = 2 sen x cos x. cos(2x) = cos ^2 (x) - sen ^2 (x) = 2 cos ^2 (x) - 1 = 1 - 2 sen ^2 (x). tan(2x) = 2 tan(x) / (1 Figure 14.4.4: Linear approximation of a function in one variable. The tangent line can be used as an approximation to the function f(x) for values of x reasonably close to x = a. When working with a function of two variables, the tangent line is replaced by a tangent plane, but the approximation idea is much the same. NCERT Solutions for Class 10 Science. NCERT Solutions for Class 10 Science Chapter 1; NCERT Solutions for Class 10 Science Chapter 2; NCERT Solutions for Class 10 Science Chapter 3 Explanation: We cannot simply apply the sum formula as tan(x + π 2) = tanx +tan(π 2) 1 − tanxtan( π 2) because tan( π 2) does not exist. But we can rewrite x + π 2 = (x + π 4) + π 4 and apply the sun formula twice. We can not simply use the tangent of a sum formula, because tan (pi/2) does not exist. See other answer for using the sum Each trigonometric function in terms of each of the other five. [1] in terms of. sin ⁡ θ {\displaystyle \sin \theta } csc ⁡ θ {\displaystyle \csc \theta } cos ⁡ θ {\displaystyle \cos \theta } sec ⁡ θ {\displaystyle \sec \theta } tan ⁡ θ {\displaystyle \tan \theta } cot ⁡ θ {\displaystyle \cot \theta } Solution. First, apply the addition formula and expand 3θ to 2θ and θ. Then, apply double angle formulas for sine and cosine. Once done, multiply each like term to shorten the equation. Notice that you can utilize the Pythagorean identity sin 2 θ + cos 2 θ = 1. Finally, simplify the equation to its lowest term. Let us consider two lines with slopes m1 m 1, and m2 m 2 respectively. The acute angle θ between the lines can be calculated using the formula of the tangent function. The acute angle between the two lines is given by the following formula. tan θ = ∣∣ ∣ m1 −m2 1+m1m2 ∣∣ ∣ | m 1 − m 2 1 + m 1 m 2 |. Further, we can find the 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. cot( − θ) = − cotθ. OrSgSn.

2 tan a tan b formula