Falling Behind in Studies? Join Our Performance Improvement Batch. Enroll For Free
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
prove that: i. cosec2A - cot2A = tanA ii. 2sinAcos 3 A - 2sin 3 AcosA = sin4A/2
1) COSEC2A - COT2A = TANA LHS= 1/SIN2A - COS2A/SIN2A =1-COS2A/SIN2A COS2A = 1-2SIN2A & sin2a =2SINACOSA , BY USING THESE LHS= [1- (1-2SIN2A)]/2SINACOSA =2SIN2A/2SINACOSA=SINA/COSA =TANA = RHS HENCE PROVED
1) COSEC2A - COT2A = TANA
LHS= 1/SIN2A - COS2A/SIN2A
=1-COS2A/SIN2A
COS2A = 1-2SIN2A & sin2a =2SINACOSA , BY USING THESE
LHS= [1- (1-2SIN2A)]/2SINACOSA
=2SIN2A/2SINACOSA=SINA/COSA
=TANA = RHS
HENCE PROVED
2) 2SINACOS3A - 2SIN3ACOSA = SIN4A/2 LHS =2SINACOSA(COS2A - SIN2A) COS2A - SIN2A =COS2A & 2SINACOSA =SIN2A LHS =SIN2ACOS2A =(2SIN2ACOS2A)/2 =SIN4A/2 (using sin2x = 2sinxcosx) hence proved
2)
2SINACOS3A - 2SIN3ACOSA = SIN4A/2
LHS =2SINACOSA(COS2A - SIN2A)
COS2A - SIN2A =COS2A & 2SINACOSA =SIN2A
LHS =SIN2ACOS2A
=(2SIN2ACOS2A)/2
=SIN4A/2 (using sin2x = 2sinxcosx)
hence proved
Cosec2A= cot2A+tanA=> RHS=cot2A+tanACos2A/sin2A+sinA/cosACos2A*cosA+sin2A*sinA/sin2A.cosaCos(2A-A)/sin2A.cosACosA/sin2A.cosA1/sin2A=cosec2A
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -