Question: If $\pi = 180°$, verify that: $tan^2 \frac{\pi}{3} - cos^2\frac{\pi}{3} = \dfrac{sin^2 \frac{\pi}{3} - cos^4 \frac{\pi}{3}}{cos^2 \frac{\pi}{3}}$. Solution: We know, $\pi = 180°$ To verify:  $tan^2 \frac{\pi}{3} - cos^2\frac{\pi}{3} = \dfrac{sin^2 \frac{\pi}{3} - cos^4 \frac{\pi}{3}}{cos^2…

Question: If $\pi = 180°$, find the value of $tan \frac{\pi}{3}.sin\frac{\pi}{6} + sin\frac{\pi}{4}.cos\frac{\pi}{2} + cos\frac{\pi}{2}.sin\frac{\pi}{3}$. Answer: $\dfrac{\sqrt{3}}{2}$ Solution: Given, $\pi = 180°$ Now, $= tan \frac{\pi}{3}.sin\frac{\pi}{6} + sin\frac{\pi}{4}.cos\frac…

If $tanA = \dfrac{x}{y}$, find the value of $\dfrac{xsinA - ycosA}{xsinA + ycosA}$.  Solution: Given, $tan A = \dfrac{x}{y}$ To find: $\dfrac{xsinA - ycosA}{xsinA + ycosA} = ?$ Now, $= \dfrac{xsinA - ycosA}{xsinA + ycosA}$ [Dividing by cosA] $= \dfrac{ \frac{xsinA}{cosA} - \frac{ycosA}{cosA}}{\frac{xsinA}{cosA} + \frac{ycosA}{cosA}}…

Prove that: cos 15° . sin 75° = $\dfrac{2+\sqrt{3}}{4}$ | SciPiPupil This is a class 10 Question From Trigonometric Identities chapter of Unit Trigonometry. All the steps for the solutions are mentioned as hint.  Solution : In this solution, We have used the following trigonometric ratios obtained by the transformation of existing t…

Prove that: $cos^320° +sin^310° = \frac{3}{4}(cos20°+sin10°)$ Solution: We know, $cos3A = 4cos^3A-3cosA$ or, $4cos^3A = cos3A +3cosA$ or, $cos^3A = \frac{cos3A+3cosA}{4}$ Taking A = 20° $cos^320° = \frac{cos60°+3cos20°}{4} \;--(i)$ Also, $sin3B = 3sinB -4sin^3B$ or, $4sin^3B = 3sinB -sin3B$ or, $sin^3B = \frac{3sinB- sin3B}{4}$ Taki…

Prove that : $\dfrac{1}{sin10°} - \dfrac{\sqrt 3}{cos10°} = 4$ This is a class 10 Question From Values of Trigonometric Ratios chapter of Unit Trigonometry. All the steps for the solutions are mentioned in the  description below . If that's hard for you to navigate, you can always visit the facebook link given at the end of ever…

Prove that: 2tan50° +tan20° = cot20° Answer: I  call this question neither as tricky nor as hard but serious. Because you need to be serious on every of your steps in this question! We knew that, cot20°= tan70° So, the first thing we did is find the common relation between the LHS and the RHS. Since we got the relation, 50°+20°=70°,…

Prove that: (tan4A-tan3A)/(1+ tan4A.tan3A) = tanA  Answer: This question might seem difficult at the first glance. So, what I suggest is: 'Take the problem easily but seriously.' Therefore, look for the possibilities. When I looked, I knew the formula of tan2A and tanA but I had not read the use of tan4A nor tan3A. Then, I l…

Prove that: sin^2(45°+Θ) +sin^2(45°-Θ) = 1   ANSWER: You need to first understand the formula of compound angles in order to solve such Trigonometric questions for compound angles in Trigonometry of Mathematics. And after you apply the formula, you can simply square the given formula as Sin²(a+b) = {sin(a+b)}² And, Sin²(a-b) = {sin(…

Prove that: cos(45°+A) - sin(45°-A) = 0 Answer: You need to understand the given formulas of compound angles to be able to solve the problems related to Trigonometric Ratios of Compound Angles in Trigonometry of Mathematics. Question: Prove that: cos(45°+A) - sin(45°-A) = 0 | Trigonometric Ratios of Compound Angles | SciPiPupil #Sci…

Find the value of: Cos20° + cos40° + cos140° + cos160° Answer: I won't explain the answer but rather show you the values of them. Once you put the value of sin and cos as indicated in the question and perform the basic Mathematics, you will get your answer. Also, you need to understand these formulas (a part of CAST formula) You…