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Example

Example. Prove that 1 – cos2X = tanX sin2X. **********. LHS = 1 – cos2X sin2X. use 3 rd formula. = 1 – ( 1- 2sin 2 X) 2sinXcosX. = 2sinXsinX 2sinXcosX. = sinX cosX. = tanX. = RHS. Example.

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Example

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  1. Example Prove that 1 – cos2X = tanX sin2X ********** LHS =1 – cos2X sin2X use 3rd formula = 1 – ( 1- 2sin2X) 2sinXcosX = 2sinXsinX 2sinXcosX = sinX cosX = tanX = RHS

  2. Example Given that  is acute and sin = 8/17 then find the exact values of (i) cos (ii) sin2 (iii) cos2 (iv) tan2 ********* (i) cos2 = 1 – sin2 (ii) sin2 = 2sincos = 1 – (8/17)2 = 2/1 X 8/17 X 15/17 = 1 – 64/289 = 240/289 = 225/289 cos = +/- (225/289) = 15/17 since  acute over

  3. (iii) cos2 = cos2 - sin2 (iv) tan2 = sin2 cos2 = (15/17)2 – (8/17)2 = 240/289  161/289 = 225/289 - 64/289 1 = 240/289 X 289/161 = 161/289 1 = 240/161

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