Trigonometry

Question : Prove that tan pi/20.tan 3pi/20.tan 5pi/20.tan 7pi/20.tan 9pi/20=1 Solution : To prove that tan pi/20.tan 3pi/20.tan 5pi/20.tan 7pi/20.tan 9pi/20=1 LHS \[tan\frac{\pi}{20}.tan\frac{3\pi}{20}.\tan{\frac{5\pi}{20}}.tan\frac{7\pi}{20}.tan\frac{9\pi}{20}\] Since \[\tan{\frac{5\pi}{20}}\ =\tan{\frac{\pi}{4}}=1\] \[ tan\frac{\pi}{20}.tan\frac{3\pi}{20}.tan\frac{7\pi}{20}.tan\frac{9\pi}{20}\] \[tan\frac{\pi}{20}.tan\frac{9\pi}{20}.tan\frac{3\pi}{20}.tan\frac{7\pi}{20}\] \[\left(tan\frac{\pi}{20}.tan\frac{9\pi}{20}\right).\left(tan\frac{3\pi}{20}.tan\frac{7\pi}{20}\right)\]…

Question : Prove that cot pi/20.cot 3pi/20.cot 5pi/20.cot 7pi/20.cot 9pi/20=1 Solution : To prove that cot pi/20.cot 3pi/20.cot 5pi/20.cot 7pi/20.cot 9pi/20=1 LHS \[cot\frac{\pi}{20}.cot\frac{3\pi}{20}.cot\frac{5\pi}{20}.cot\frac{7\pi}{20}.cot\frac{9\pi}{20}\] Since \[cot\frac{5\pi}{20}=\cot{\frac{\pi}{4}}=1\] \[cot\frac{\pi}{20}.cot\frac{3\pi}{20}.cot\frac{7\pi}{20}.cot\frac{9\pi}{20}\] \[cot\frac{\pi}{20}.cot\frac{9\pi}{20}.cot\frac{3\pi}{20}.cot\frac{7\pi}{20}\] \[\rightarrow \left(cot\frac{\pi}{20}.cot\frac{9\pi}{20}\right).\left(cot\frac{3\pi}{20}.cot\frac{7\pi}{20}\right)\] By…

Question :  how to prove Pythagorean Identities?  Solution : There are three Pythagorean Identities sin²𝜃 + cos²𝜃 = 1  1+ tan²𝜃 = sec²𝜃 1+ cot²𝜃 = csc² 𝜃 Proof :…

Question : What are Reciprocal of trigonometric functions. Use them to find exact values of the following expressions tan 45° − 1/ cot 45°  cot 30° ⋅ sec 30° ⋅…

Question :  How do you convert radian to degree? Convert the following angles in radian to degree. 3𝜋/2 - 5𝜋/3  13𝜋/4 -7𝜋/6 Answer : convert radian to degree : We…

how to convert radian to degrees ?? Answer : Convert degree to radian Since 1 revolution in a unit circle satisfies  360° = 2π radians   Dividing by 2 both…

Question : If cosec θ +cot θ =1/5. Find the quadrant in which θ lies and the value of cos θ Solution :

Question: how to find the value of sin(75)? Solution : We shall write 750=450+300 And apply Sin(A+B)  formula Sin(A+B) =Sin(A)Cos(B)+Cos(A)Sin(A) Therefore Sin(750) = Sin(450+300) =Sin(450)Cos(300)+Cos(450)Sin(300)  Now we shall substitute following…

Question: how to find the value of sin(15)? Solution : We shall write 150=450-300 And apply Sin(A-B)  formula Sin(A-B) =Sin(A)Cos(B)-Cos(A)Sin(A) Therefore Sin(150) = Sin(450-300) =Sin(450)Cos(300)-Cos(450)Sin(300)  Now we shall substitute following…