Dear student, LHS = 1 + cot θ - cosec θ 1 + tan θ + sec θ=1 + cos θsin θ - 1sin θ 1 + sin θcos θ + 1cos θ=sin θ + cos θ - 1sin θ cos θ + sin θ + 1cos θ=sin θ + cos θ2 - 12sin θ cos θ=sin2θ + cos2θ + 2 sin θ cos θ - 1sin θ cos θ =sin2θ + cos2θ + 2 sin θ cos θ - 1sin θ cos θ=1 + 2 sin θ cos θ - 1 sin θ cos θ=2 sin θ cos θ sin θ cos θ=2= RHS Hence proved Regards

Please solve Q. No.5

Dear student,

LHS = (1 + \cot θ - cosec θ) (1 + \tan θ + \sec θ) = (1 + \frac{\cos θ}{\sin θ} - \frac{1}{\sin θ}) (1 + \frac{\sin θ}{\cos θ} + \frac{1}{\cos θ}) = (\frac{\sin θ + \cos θ - 1}{\sin θ}) (\frac{\cos θ + \sin θ + 1}{\cos θ}) = \frac{{(\sin θ + \cos θ)}^{2} - {(1)}^{2}}{\sin θ \cos θ} = \frac{\sin^{2} θ + \cos^{2} θ + 2 \sin θ \cos θ - 1}{\sin θ \cos θ} = \frac{(\sin^{2} θ + \cos^{2} θ) + 2 \sin θ \cos θ - 1}{\sin θ \cos θ} = \frac{1 + 2 \sin θ \cos θ - 1}{\sin θ \cos θ} = \frac{2 \sin θ \cos θ}{\sin θ \cos θ} = 2 = RHS

Hence proved
Regards

View Full Answer