Q. 135.0( 2 Votes )

Evaluate : cos105

Answer :

formula: - (i) cos(A + B) = cosAcosB - sinAsinB


(ii) sin(A + B) = sinAcosB + cosAsinB


(iii) sin(A – B) = sinAcosB – cosAsinB


(iv) cos(A – B) = cosAcosB + sinAsinB


cos 105° + sin 105° = Cos(90° + 15°) + sin(90° + 15°)


using formula (i) and (ii)


cos 105° + sin 105° = Cos90°cos15° – sin90°sin15° + sin90°cos15° + cos90°sin15°


cos 105° + sin 105° = 0 – sin15° + cos15° + 0


cos 105° + sin 105° = – sin(45° – 30°) + cos(45° – 30°)


using formula (iii) and (iv)


cos 105° + sin 105° = – sin45°cos30° + cos45°sin30° + cos45°cos30° + sin45°sin30°


cos 105° + sin 105°


cos 105° + sin 105°


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