1800-150-456-789
FlagBACK
Flag Trigonometry> (1 / sec a – tan a )–( 1 / cos a )= (1/ c...
question mark

(1 / sec a – tan a )–( 1 / cos a )= (1/ cos a) –( 1/ sec a + tan a) prove it.

Prateek Agrawal , 10 Years ago
Grade 12
anser 2 Answers
Kaustubh Nayyar

Last Activity: 10 Years ago

LHS=1/seca-tana   –   1/cosa
       = cosa /(1- sina) – 1/cosa =  (cos2a – (1 – sina))/(1 – sina)(cosa)
        = (sina – sin2a)/(1 – sina)(cosa) = (sina)(1 – sina)/(1 – sina)(cosa)
       =  tana
RHS=1/cosa – 1/(seca+tana)  =  (1/cosa) –( cosa/(sina+1))
       =  (sina +1  – cos2a)/(cosa)(sina+1)  =  (sina +1 +sin2a – 1)/(sina+1)(cosa)
       = sina/cosa = tana

Kushagra Madhukar

Last Activity: 4 Years ago

Dear student,
Please find the solution to your problem.
 
LHS = 1/(seca-tana) – 1/cosa
       = cosa /(1 – sina) – 1/cosa
       =  (cos2a – (1 – sina))/(1 – sina)(cosa)
       = (sina – sin2a)/(1 – sina)(cosa)
       = (sina)(1 – sina)/(1 – sina)(cosa)
       =  tana
 
RHS = 1/cosa – 1/(seca+tana)  
        =  (1/cosa) – ( cosa/(sina+1))
        =  (sina +1  – cos2a)/(cosa)(sina+1)  
        =  (sina +1 +sin2a – 1)/(sina+1)(cosa)
        = sina/cosa
        = tana
 
Hence, LHS = RHS
Hence proved.
 
Thanks and regards,
Kushagra

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Other Related Questions on trigonometry

question mark
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
1 Answer Available

Last Activity: 2 Years ago

question mark
  • Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
trigonometry
0 Answer Available

Last Activity: 3 Years ago

question mark
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
trigonometry
0 Answer Available

Last Activity: 3 Years ago

question mark
cos^2 13ºcos^2 47º+cos^2 73º =? …..................
trigonometry
0 Answer Available

Last Activity: 3 Years ago

question mark
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
0 Answer Available

Last Activity: 3 Years ago