(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
Trigonometry> (1 / sec a – tan a )–( 1 / cos a )= (1/ c...
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
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on Trigonometry
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 Year ago(s)
Find the general solution of equation tan3∂=cot2∂For all angles between -720 and +720
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)
cos^2 13ºcos^2 47º+cos^2 73º =? …..................
Trigonometry
0 Answer Available
Last Activity: 2 Year ago(s)
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: 2 Year ago(s)