(1+tan theta+sec theta)(1+cot theta-operatorn | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given expression: $(1+	an 	heta+\sec 	heta)(1+\cot 	heta-\operatorname{cosec} 	heta)$Convert the trigonometric ratios into $\sin 	heta$ and

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) Given expression: $(1+	an 	heta+\sec 	heta)(1+\cot 	heta-\operatorname{cosec} 	heta)$Convert the trigonometric ratios into $\sin 	heta$ and $\cos 	heta$:$= \left(1 + \frac{\sin 	heta}{\cos 	heta} + \frac{1}{\cos 	heta}ight) \left(1 + \frac{\cos 	heta}{\sin 	heta} - \frac{1}{\sin 	heta}ight)$Simplify the terms inside the brackets:$= \left(\frac{\cos 	heta + \sin 	heta + 1}{\cos 	heta}ight) \left(\frac{\sin 	heta + \cos 	heta - 1}{\sin 	heta}ight)$Apply the algebraic identity $(a+b)(a-b) = a^2 - b^2$,where $a = (\sin 	heta + \cos 	heta)$ and $b = 1$:$= \frac{(\sin 	heta + \cos 	heta)^2 - (1)^2}{\sin 	heta \cos 	heta}$Expand the numerator using $(a+b)^2 = a^2 + b^2 + 2ab$:$= \frac{\sin^2 	heta + \cos^2 	heta + 2 \sin 	heta \cos 	heta - 1}{\sin 	heta \cos 	heta}$Using the identity $\sin^2 	heta + \cos^2 	heta = 1$:$= \frac{1 + 2 \sin 	heta \cos 	heta - 1}{\sin 	heta \cos 	heta}$$= \frac{2 \sin 	heta \cos 	heta}{\sin 	heta \cos 	heta} = 2$

$(1+\tan \theta+\sec \theta)(1+\cot \theta-\operatorname{cosec} \theta) = \dots$

Similar Questions

Given $15 \cot A = 8$,find $\sin A$ and $\sec A$.

Evaluate the following:
$\frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}}$ (in $/12$)

State whether the following is true or false. Justify your answer.
$\sin \theta = \cos \theta$ for all values of $\theta$.

If $\tan (A + B) = \sqrt{3}$ and $\tan (A - B) = \frac{1}{\sqrt{3}}$,where $0^{\circ} < A + B \leq 90^{\circ}$ and $A > B$,find the values of $A$ and $B$.

If $\sin A = \frac{3}{4},$ calculate $\cos A$ and $\tan A$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module