Question

Out of the following four relations:
(I) $\frac{sinA}{1+cosA}$+ $\frac{sinA}{1-cosA}$= $\frac{2}{sinA}$
(II) ${\left(\frac{1+cosA}{sinA}\right)}^2$ = $\frac{1+cosA}{1-cosA}$
(III) $\frac{sin{10}^o}{cos{80}^o}$ = 1
(Iv) $si{n}^{4}A-co{s}^{4}A=1+si{n}^{2}A$
the wrong one is

• A. I
• B. II
• C. III
• D. IV

Answer 1

Answer: (D)

IV

The wrong one is Option D
$si{n}^{4}A-co{s}^{4}A=(si{n}^{2}A{)}^2-(co{s}^{4}A{)}^2$
$=(si{n}^{2}A-co{s}^{2}A)(si{n}^{2}A+co{s}^{2}A)$
$=(si{n}^{2}A-co{s}^{2}A)$ [using, $si{n}^2\theta +co{s}^2\theta =1$]
$=si{n}^{2}A-(1-si{n}^{2}A)$
$=2si{n}^{2}A-1$
$\therefore$ Option D is correct answer.