A) \[a+b\]
B) \[ab\]
C) \[{{a}^{2}}+{{b}^{2}}\]
D) \[{{a}^{2}}-{{b}^{2}}\]
Correct Answer: C
Solution :
Given, p = a sin x + b cos x and g \[=a\text{ }cosx-\text{ }b\text{ }sinx\] \[\Rightarrow ~{{p}^{2}}=\text{ }{{a}^{2}}si{{n}^{2}}x\text{ }+\text{ }{{\text{b}}^{2}}co{{s}^{2}}x\text{ }+\text{ }2ab\text{ }sin\] \[x\,cos\,x\,and\text{ }{{q}^{2}}=\text{ }{{a}^{2}}co{{s}^{2}}x\text{ }+\text{ }{{b}^{2}}si{{n}^{2}}x\text{ }-\] \[2ab\text{ }sinx\,cos\,x\] \[{{p}^{2}}+\text{ }{{q}^{2}}=\text{ }{{a}^{2}}(si{{n}^{2}}x\text{ }+\text{ }co{{s}^{2}}x+\text{ }{{b}^{2}}(co{{s}^{2}}x\text{ }+\] \[si{{n}^{2}}x)\Rightarrow ~{{p}^{2}}+{{q}^{2}}=\]
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