Prave that:(1) sin2θcosθ+cosθ=secθ(2) cos2θ1+tan2θ=1(3) 1-sinθ1+sinθ=secθ-tanθ(4) secθ-cosθcotθ+tanθ=tanθ secθ(5) cotθ+tanθ=cosecθ secθ(6) 1secθ-tanθ=secθ+tanθ(7) sec4θ-cos4θ=1-2cos2θ(8) secθ+tanθ=cosθ1-sinθ(9) If tanθ+1tanθ=2, then show that tan2θ+1tan2θ=2(10) tanA1+tan2A2+cotA1+cot2A2=sin A cos A(11) sec4A1-sin4A-2tan2A=1(12) tanθsecθ-1=tanθ+secθ+1tanθ+secθ-1

Prave that:(1) sin2θcosθ+cosθ=secθ(2) cos2θ1+tan2θ=1(3) 1-sinθ1

1.	Prave that:(1) sin2θcosθ+cosθ=secθ(2) cos2θ1+tan2θ=1(3) 1-sinθ1+sinθ=secθ-tanθ(4) secθ-cosθcotθ+tanθ=tanθ secθ(5) cotθ+tanθ=cosecθ secθ(6) 1secθ-tanθ=secθ+tanθ(7) sec4θ-cos4θ=1-2cos2θ(8) secθ+tanθ=cosθ1-sinθ(9) If tanθ+1tanθ=2, then show that tan2θ+1tan2θ=2(10) tanA1+tan2A2+cotA1+cot2A2=sin A cos A(11) sec4A1-sin4A-2tan2A=1(12) tanθsecθ-1=tanθ+secθ+1tanθ+secθ-1
Answer» Prave that: (1) $\frac{\sin^{2} θ}{cosθ} + cosθ = secθ$ (2) $\cos^{2} θ (1 + \tan^{2} θ) = 1$ (3) $\sqrt{\frac{1 - sinθ}{1 + sinθ}} = secθ - tanθ$ (4) $(secθ - cosθ) (cotθ + tanθ) = tanθ secθ$ (5) $cotθ + tanθ = cosecθ secθ$ (6) $\frac{1}{secθ - tanθ} = secθ + tanθ$ (7) $\sec^{4} θ - \cos^{4} θ = 1 - 2 \cos^{2} θ$ (8) $secθ + tanθ = \frac{\cos θ}{1 - sinθ}$ (9) If $t anθ + \frac{1}{tanθ} = 2$ , then show that $\tan^{2} θ + \frac{1}{\tan^{2} θ} = 2$ (10) $\frac{tanA}{{(1 + \tan^{2} A)}^{2}} + \frac{cotA}{{(1 + \cot^{2} A)}^{2}} = \sin A \cos A$ (11) $\sec^{4} A (1 - \sin^{4} A) - 2 \tan^{2} A = 1$ (12) $\frac{tanθ}{secθ - 1} = \frac{tanθ + secθ + 1}{tanθ + secθ - 1}$