math

How would you establish this identity:

(1+sec(beta))/(sec(beta))=(sin^2(beta))/(1-cos(beta))

on the right, sin^2 = 1-cos^2, that factor to 1-cos * `1+cos, then the denominator makes the entire right side 1+cosB
which is 1+1/sec which is 1/sec (sec+1)

qed

using sec(beta) = 1/cos(beta):

1+sec(beta))/(sec(beta))= 1 + cos(beta)

sin^2(beta)/(1-cos(beta)) =

(1-cos^2(beta))/(1-cos(beta)) =

1 + cos(beta)

This follows e.g. from:

(1 - x^2) = (1 - x)(1 + x)

and thus:

(1 - x^2)/(1 - x) = 1 + x

  1. 👍 0
  2. 👎 0
  3. 👁 137
  1. x=(-1)

    1. 👍 0
    2. 👎 0
    posted by rahul

Respond to this Question

First Name

Your Response

Similar Questions

  1. trig

    verify the identity: sec(beta)+ tan (beta)= cos(beta)/ 1-sin(beta)

    asked by stacey graham on March 26, 2010
  2. Trigonometry

    Prove that tan (Beta) sin (Beta) + cos (Beta) = sec (Beta) Please explain.

    asked by Cynthia on August 3, 2012
  3. pre calc

    suppose beta is an angle in the second quadrant and tan beta=-2. Fine the exact vaule of sin beta and cos beta

    asked by Danika on April 7, 2010
  4. trig

    evaluate the following in exact form, where the angeles alpha and beta satisfy the conditions: sin alpha=4/5 for pi/2 < alpha < pi tan beta=7/24 for pie < beta < 3pi/2 answer choices A. sin(beta+alpha) B. tan(beta-alpha) C.

    asked by liyah on December 13, 2012
  5. Math

    using sin(alpha-beta)=(sin alpha)(cos beta)-(cos alpha)(sin beta) use the identity to derive the result proof for : sin(alpha-beta) PLEASE PLEASE PLEASE HELP

    asked by Mari on July 29, 2014
  6. maths

    prove that the length of the perpendicular from the origin to the straight line joining the two points having coordinates ( a cos alpha, a sin alpha) and (a cos beta, a sin beta) is a cos { ( alpha + beta)/2}.

    asked by Anonymous on January 23, 2013
  7. Physics Important please

    A yo-yo of mass m rests on the floor (the static friction coefficient with the floor is mu ). The inner (shaded) portion of the yo-yo has a radius R-1 , the two outer disks have radii R-2 . A string is wrapped around the inner

    asked by rosa on November 12, 2013
  8. Physics Important please

    A yo-yo of mass m rests on the floor (the static friction coefficient with the floor is mu ). The inner (shaded) portion of the yo-yo has a radius R-1 , the two outer disks have radii R-2 . A string is wrapped around the inner

    asked by rosa on November 12, 2013
  9. Physics Important please

    A yo-yo of mass m rests on the floor (the static friction coefficient with the floor is mu ). The inner (shaded) portion of the yo-yo has a radius R-1 , the two outer disks have radii R-2 . A string is wrapped around the inner

    asked by rosa on November 13, 2013
  10. Physics Important please

    A yo-yo of mass m rests on the floor (the static friction coefficient with the floor is mu ). The inner (shaded) portion of the yo-yo has a radius R-1 , the two outer disks have radii R-2 . A string is wrapped around the inner

    asked by rosa on November 12, 2013

More Similar Questions