Question

$(sinA+cosecA{)}^2+(cosA+secA{)}^2=$

• A. $7+ta{n}^{2}A+se{c}^{2}A$
• B. $11+ta{n}^{2}A+co{t}^{2}A$
• C. $9+ta{n}^{2}A+co{t}^{2}A$
• D. $7+ta{n}^{2}A+co{t}^{2}A$

Answer 1

The correct option is D

$7+ta{n}^{2}A+co{t}^{2}A$

$(sinA+cosecA{)}^2+(cosA+secA{)}^{2}L.H.S=(sinA+cosecA{)}^2+(cosA+secA{)}^2=(si{n}^{2}A+cose{c}^{2}A+2sinAcosecA)+(co{s}^{2}A+se{c}^{2}A+2cosAsecA)=(si{n}^{2}A+co{s}^{2}A)+2sinA\left(\frac{1}{sinA}\right)+2cosA\left(\frac{1}{cosA}\right)+1+ta{n}^{2}A+1+co{t}^{2}A=1+2+2+2+ta{n}^{2}A+co{t}^{2}A=7+ta{n}^{2}A+co{t}^{2}A=R.H.S$