Verify the identity `sin x/sec x = 1/(tanx+cotx)`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The identity `sin x/sec x = 1/(tanx+cotx)` has to be verified

`1/(tan x+cot x)`

=> `1/(sin x/cos x + cos x/sin x)`

=> `1/((sin^2x + cos^2x)/(sin x*cos x))`

=> `sin x*cos x`

=> `sin x/sec x`

This proves that `sin x/sec x = 1/(tanx+cotx)`

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