| What is the value of \[\sin A+\cos A\tan A+\cos A\sin A\cot A?\] [CDS 2012] |
A) \[{{\sin }^{2}}A+\cos A\]
B) \[{{\sin }^{2}}A+{{\tan }^{2}}A\]
C) \[{{\sin }^{2}}A+{{\cot }^{2}}A\]
D) \[\text{cose}{{\text{c}}^{2}}A-{{\cot }^{2}}A\]
Correct Answer: D
Solution :
| \[\sin A\cos A\tan A+\cos A\sin A\cot A\] |
| \[=\sin A\cos A\frac{\sin A}{\cos A}+\cos A\sin A\frac{\cos A}{\sin A}\] |
| \[={{\sin }^{2}}A+{{\cos }^{2}}A=1\]\[[\because {{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1]\] |
| \[=\text{cose}{{\text{c}}^{2}}A-{{\cot }^{2}}A\]\[[\because 1+{{\cot }^{2}}\theta =\text{cose}{{\text{c}}^{2}}\theta ]\] |
You need to login to perform this action.
You will be redirected in
3 sec
