1-sin2A/cos2A=1-tanA/1+tanA
Answers
=cos^2A +sin^2A-2sinAcosA/
cos^2A-sin^2A
= cos^2A-2sonAcosA+sin^2A/
cos^2A-sin^2A
= (cosA +sinA)^2/ (cosA - sinA)
(cosA+sinA)
= (cosA +sinA) (cosA+sinA)/
(cosA-sinA)(cosA+sinA)
= [(cosA+sinA)/(cosA-sinA)]÷cosA
=1+(sinA/cosA) /1-(sinA/cosA)
=1+tanA/1-tanA.
hence it is proved.
Answer:
1+tanA/1-tanA
Step-by-step explanation:
Given:
Trigonometric equation 1-sin2A/cos2A=1-tanA/1+tanA
To find:
The value of the trigonometric equation 1-sin2A/cos2A=1-tanA/1+tanA
Solution:
Sine Angle: Sine is a trigonometric function of an angle defined as the length of the perpendicular (opposite) side divided by the length of the hypotenuse.
Cosine Angle: The trigonometric function equal to the side adjacent to an acute angle (in a right-angled triangle) divided by the hypotenuse.
1-sin2A/cos2A = 1-2sinA.cosA/cos^2A-sin^2A
=cos^2A +sin^2A-2sinAcosA/cos^2A-sin^2A
= cos^2A-2sonAcosA+sin^2A/cos^2A-sin^2A
= (cosA +sinA)^2/ (cosA - sinA)(cosA+sinA)
= (cosA +sinA) (cosA+sinA)/(cosA-sinA)(cosA+sinA)
= [(cosA+sinA)/(cosA-sinA)]÷cosA
=1+(sinA/cosA) /1-(sinA/cosA)
=1+tanA/1-tanA.
Hence, the value of 1-sin2A/cos2A=1-tanA/1+tanA = 1+tanA/1-tanA.
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