A) -1
B) 0
C) \[se{{c}^{2}}x\]
D) 1
Correct Answer: D
Solution :
(d):\[{{\left( secx.secy+tanx.tany \right)}^{2}}-\left( secx.tany+tanx.secy \right)\] \[=se{{c}^{2}}x.se{{c}^{2}}y+ta{{n}^{2}}x.ta{{n}^{2}}y+2secx.secy.tanx.tany-\] \[se{{c}^{2}}x.ta{{n}^{2}}y-ta{{n}^{2}}x.se{{c}^{2}}y-2secx.secy.tanx.tany\] \[=se{{c}^{2}}x.\text{ }se{{c}^{2}}y-se{{c}^{2}}x.ta{{n}^{2}}y-ta{{n}^{2}},se{{c}^{2}}y+ta{{n}^{2}}x.ta{{n}^{2}}y\] \[=se{{c}^{2}}x\left( se{{c}^{2}}y-ta{{n}^{2}}y \right)-ta{{n}^{2}}x\left( se{{c}^{2}}y-ta{{n}^{2}}y \right)\] \[=se{{c}^{2}}x-ta{{n}^{2}}x=1\]
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