cosA / 1 - sinA = tan (45 + A/2)

Question

Sam Abraham · Answer

CosA / 1 – SinA can be written as Cos2A/2 – Sin2A/2 / Cos2A + Sin2A/2 +2Sin A/2 Cos A/2 ….… which is equal to = Cos2A/2 – Sin2A/2 / (CosA/2 + SinA/2)2 .. As Sin2A/2 +2Sin A/2 Cos A/2 is in the form of X2 + Y2 +2XY = (X+Y)2 And Cos2A/2 – Sin2A can be written as (CosA/2 – SinA/2) (CosA/2 + SinA/2) .. as it is in the form of (X + Y)(X – Y ) = X2 – Y2 So Cos2A/2 – Sin2A/2 / Cos2A + Sin2A/2 +2Sin A/2 Cos A/2 = (CosA/2 – SinA/2) (CosA/2 + SinA/2) / (CosA/2 + SinA/2) 2 = (CosA/2 – SinA/2) (CosA/2 + SinA/2) / (CosA/2 + SinA/2) 2 = (CosA/2 – SinA/2) / (CosA/2 + SinA/2) . Now divide the numerator and the denominator by CosA/2 .. because of which we get .. 1 – tan A/2 / 1 + tan A/2 = tan 45 + tan A/2 / 1 – tan 45 * tan A/2 = tan (45 +A/2) . Guess it helped . :)

Sam Abraham · Answer

CosA / 1 – SinA can be written as Cos 2 A/2 – Sin 2 A/2 / Cos 2 A/2 + Sin 2 A/2 +2Sin A/2 Cos A/2 ….… which is equal to = Cos 2 A/2 – Sin 2 A/2 / (CosA/2 + SinA/2) 2 .. As Sin 2 A/2 + Cos 2 A/2 + 2Sin A/2 Cos A/2 is in the form of X 2 + Y 2 +2XY = (X+Y) 2 And Cos 2 A/2 – Sin 2 A/2 can be written as (CosA/2 – SinA/2) (CosA/2 + SinA/2) .. as it is in the form of (X + Y)(X – Y ) = X 2 – Y 2 So Cos 2 A/2 – Sin 2 A/2 / Cos 2 A/2 + Sin 2 A/2 +2Sin A/2 Cos A/2 = (CosA/2 – SinA/2) (CosA/2 + SinA/2) / (CosA/2 + SinA/2) 2 = (CosA/2 – SinA/2) (CosA/2 + SinA/2) / (CosA/2 + SinA/2) 2 = (CosA/2 – SinA/2) / (CosA/2 + SinA/2) . Now divide the numerator and the denominator by CosA/2 .. because of which we get .. 1 – tan A/2 / 1 + tan A/2 = tan 45 + tan A/2 / 1 – tan 45 * tan A/2 = tan (45 +A/2) . Guess it helped . :) Revised Answer

grenade · Answer

Use the RHS as a hint how to proceed. sinA = 2sin(A/2)cos(A/2) cosA = 2cos^2 (A/2) - 1 sinA / (1+cosA) = sin(A/2) / cos(A/2) = tan(A/2)

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

cosA / 1 - sinA = tan (45 + A/2)

cosA / 1 - sinA = tan (45 + A/2)

3 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Trigonometry

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship