The value of tan2 θ sec2 θ (cot2θ - cos2θ) is

Question

The value of tan2 θ sec2 θ (cot2θ - cos2θ) is (A) 0 (B) 1 (C) -1 (D) (1/2)

Tardigrade Admin · Accepted Answer

tan2 θ sec2 θ (cot2θ - cos2θ) = sec2 θ (tan2 θ cot2 θ - tan2 θ cos2 θ ) = sec2 θ (1-(sin2 θ /cos2 θ ) cos2 θ ) = sec2 θ (1-sin2 θ ) = sec2 θ . cos2 θ = 1

Q. The value of $t a n^{2} θ se c^{2} θ (co t^{2} θ - co s^{2} θ)$ is

$0$

$1$

$- 1$

$\frac{1}{2}$

$t a n^{2} θ se c^{2} θ (co t^{2} θ - co s^{2} θ)$
$= se c^{2} θ (t a n^{2} θ co t^{2} θ - t a n^{2} θ co s^{2} θ)$
$= se c^{2} θ (1 - \frac{s i n ^{2} θ}{co s ^{2} θ} co s^{2} θ) = se c^{2} θ (1 - s i n^{2} θ)$
$= se c^{2} θ . co s^{2} θ = 1$

Q. The value of tan2θsec2θ(cot2θ−cos2θ) is

0

1

−1

21​

tan2θsec2θ(cot2θ−cos2θ) =sec2θ(tan2θcot2θ−tan2θcos2θ) =sec2θ(1−cos2θsin2θ​cos2θ)=sec2θ(1−sin2θ) =sec2θ.cos2θ=1

Q. The value of $t a n^{2} θ se c^{2} θ (co t^{2} θ - co s^{2} θ)$ is

$0$

$1$

$- 1$

$\frac{1}{2}$

$t a n^{2} θ se c^{2} θ (co t^{2} θ - co s^{2} θ)$
$= se c^{2} θ (t a n^{2} θ co t^{2} θ - t a n^{2} θ co s^{2} θ)$
$= se c^{2} θ (1 - \frac{s i n ^{2} θ}{co s ^{2} θ} co s^{2} θ) = se c^{2} θ (1 - s i n^{2} θ)$
$= se c^{2} θ . co s^{2} θ = 1$