The value of $$\frac{{\sin {{23}^ \circ }\cos {{67}^ \circ } + \sec {{52}^ \circ }\sin {{38}^ \circ } + \cos {{23}^ \circ }\sin {{67}^ \circ } + {\text{cosec}}\,{{52}^ \circ }\cos {{38}^ \circ }}}{{{\text{cose}}{{\text{c}}^2}\,{{20}^ \circ } - {{\tan }^2}{{70}^ \circ }}}{\text{ is:}}$$
A. 3
B. 4
C. 2
D. 0
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & \frac{{\sin {{23}^ \circ }\cos {{67}^ \circ } + \sec {{52}^ \circ }\sin {{38}^ \circ } + \cos {{23}^ \circ }\sin {{67}^ \circ } + {\text{cosec}}\,{{52}^ \circ }\cos {{38}^ \circ }}}{{{\text{cose}}{{\text{c}}^2}{{20}^ \circ } - {{\tan }^2}{{70}^ \circ }}} \cr & = \frac{{{{\sin }^2}{{23}^ \circ } + \frac{1}{{\cos {{52}^ \circ }}} \times \cos {{52}^ \circ } + {{\cos }^2}{{23}^ \circ } + \frac{1}{{\sin {{52}^ \circ }}} \times \sin {{52}^ \circ }}}{{{\text{cose}}{{\text{c}}^2}{{20}^ \circ } - {{\cot }^2}{{20}^ \circ }}} \cr & = \frac{{{{\sin }^2}{{23}^ \circ } + 1 + {{\cos }^2}{{23}^ \circ } + 1}}{1}\,\,\,\,\,\left[ {\therefore \,{{\sin }^2}\theta + {{\cos }^2}\theta = 1} \right] \cr & = 1 + 1 + 1 \cr & = 3 \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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