Find the value ofsin- cos- -sin90- - - cosec- - cos90- - - sec -

Sinθ nbsp;cosθ [sin(90^∘ θ) nbsp;cosecθ + nbsp;cos(90^∘ nbsp;θ) nbsp;sec nbsp;θ] nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; ...

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Byju's Answer

Standard X

Mathematics

Trigonometric Ratio(sin,cos,tan)

Find the valu...

Question

Find the value of
$s i n θ$ $c o s θ$ [ $s i n (90^{\circ} - θ)$ $c o s e c θ$ + $c o s (90^{\circ} - θ)$ $s e c θ$ ]

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-1

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Solution

The correct option is C
1

$s i n θ$ $c o s θ$ [ $s i n (90^{\circ} - θ)$ $c o s e c θ$ + $c o s (90^{\circ} - θ)$ $s e c θ$ ]

= $s i n θ$ $c o s θ$ [ $c o s θ$ $c o s e c θ$ + $s i n θ$ $s e c θ$ ]

= $s i n θ$ $c o s θ$ [ $\frac{c o s θ}{s i n θ}$ + $\frac{s i n θ}{c o s θ}$ ]

= $s i n θ$ $c o s θ$ [ $\frac{(c o s^{2} θ + s i n^{2} θ)}{s i n θ c o s θ}$ ]

= 1

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Similar questions

Q. If

sin (90 - θ) + cos θ = \sqrt{2} cos (90 - θ)

, for

0 < θ < 90^{\circ}

, find the value of

cosec θ

Q. Evaluate:

\frac{cos θ}{sin (90^{\circ} - θ)} + \frac{sin θ}{cos (90^{\circ} - θ)}

Prove that:

(i) $s i n θ c o s (90^{\circ} - θ) + s i n (90^{\circ} - θ) c o s θ = 1$

(ii) $\frac{s i n θ}{c o s (90^{\circ} - θ)} + \frac{c o s θ}{s i n (90^{\circ} - θ)} = 2$

(iii) $\frac{s i n θ c o s (90^{\circ} - θ) c o s θ}{s i n (90^{\circ} - θ)} + \frac{c o s θ s i n (90^{\circ} - θ) s i n θ}{c o s (90^{\circ} - θ)} = 1$

(iv) $\frac{c o s (90^{\circ} - θ) s e c (90^{\circ} - θ) t a n θ}{c o s e c (90^{\circ} - θ) s i n (90^{\circ} - θ) c o t (90^{\circ} - θ)} + \frac{t a n (90^{\circ} - θ)}{c o t θ} = 2$

(v) $\frac{c o s (90^{\circ} - θ)}{1 + s i n (90^{\circ} - θ)} + \frac{1 + s i n (90^{\circ} - θ)}{c o s (90^{\circ} - θ)} = 2 c o s e c θ$

(vi) $\frac{s e c (90^{\circ} - θ) c o s e c θ - t a n (90^{\circ} - θ) c o t θ + c o s^{2} 25^{\circ} + c o s^{2} 65^{\circ}}{3 t a n 27^{\circ} t a n 63^{\circ}} = \frac{2}{3}$

(vii) $c o t θ t a n (90^{\circ} - θ) - s e c (90^{\circ} - θ) c o s e c θ + \sqrt{3} t a n 12^{\circ} t a n 60^{\circ} t a n 78^{\circ} = 2$

Q. Prove that

\frac{sin (90^{\circ} - θ)}{1 + sin θ} + \frac{cos θ}{1 - cos (90^{\circ} - θ)} = 2 sec θ

Q. Find the value of

s i n θ + c o s θ,when θ = 45^{\circ}

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Find the value of sinθ cosθ [sin(90∘−θ) cosecθ + cos(90∘−θ) secθ]

The correct option is C 1 sinθ cosθ [sin(90∘−θ) cosecθ + cos(90∘−θ) secθ] = sinθ cosθ [cosθ cosecθ + sinθ secθ] = sinθ cosθ [cosθsinθ + sinθcosθ] = sinθ cosθ [(cos2θ+sin2θ)sinθcosθ] = 1

Find the value of
$s i n θ$ $c o s θ$ [ $s i n (90^{\circ} - θ)$ $c o s e c θ$ + $c o s (90^{\circ} - θ)$ $s e c θ$ ]