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Question

How do you find a double angle formula for sec2x in terms of only cosecx and secx?


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Solution

Determine the formula using trigonometric identities:

The double angle formula for sec2x can be determined using trigonometric identities as follows,

sec2x=1cos2x [secx=1cosx]

sec2x=1cosx+x

sec2x=1cosx·cosx-sinx·sinx [cos(A+B)=cosA·cosB-sinA·sinB]

sec2x=11secx·secx-1cosecx·cosecx [cosx=1secx,sinx=1cosecx]

sec2x=11sec2x-1cosec2x

sec2x=1cosec2x-sec2xsec2x·cosec2x

sec2x=sec2x·cosec2xcosec2x-sec2x [1ab=ba]

Hence, the double angle formula for sec2x=sec2x·cosec2xcosec2x-sec2x.


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