Answered

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if cos2A= -1/2 then show that cosA=1/2​

Sagot :

swastikalamsal341

Step-by-step explanation:

If cos 2A = tan-B, then show that cos 2B = tan-A.

In ABC, prove that

cos A = 1/2 (See proof below)

[tex]cos(2A) = 2cos^{2} A-1[/tex]

Substitute  cos 2A = -1/2 into the relationship above:

[tex]\frac{-1}{2} = 2cos^{2} A - 1\\\frac{-1}{2} + 1 = 2cos^{2} A\\\frac{1}{2} = 2cos^{2} A[/tex]

Divide both sides by 2:

[tex]\frac{1}{4} = cos^{2} A[/tex]

Square root both sides:

[tex]cosA = \sqrt{\frac{1}{4} } \\cosA = \frac{1}{2}[/tex]

Proved

Learn more here: https://brainly.com/question/22852405

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