Question

sec 70° sin 20° - cos 20° cosec 70°​

Answer 1

Answer:

0

Step-by-step explanation:

Here, the given expression is,

sec 70^{\circ}.sin 20^{\circ}-cos 20^{\circ} .cosec 70^{\circ}sec70

∘

.sin20

∘

−cos20

∘

.cosec70

∘

=\frac{sin 20^{\circ}}{cos 70^{\circ}} - \frac{cos 20^{\circ}}{sin 70^{\circ} }=

cos70

∘

sin20

∘

−

sin70

∘

cos20

∘

( Because sec x = 1/cos x and cosec x = 1/sin x)

=\frac{sin 20^{\circ}}{cos (90-20)^{\circ}} - \frac{cos 20^{\circ}}{sin (90-20)^{\circ} }=

cos(90−20)

∘

sin20

∘

−

sin(90−20)

∘

cos20

∘

=\frac{sin 20^{\circ}}{sin 20^{\circ}} - \frac{cos 20^{\circ}}{cos 20^{\circ} }=

sin20

∘

sin20

∘

−

cos20

∘

cos20

∘

( Because, sin(90-x) = cos x and cos(0-x) = sin x )

=1-1=0=1−1=0

Hence,

sec 70^{\circ}.sin 20^{\circ}-cos 20^{\circ} .cosec 70^{\circ}=0sec70

∘

.sin20

−cos20

.cosec70

=0