If a -cos-cos- and b -sin-cos- then value of a - b cos- isA- cos-1-B- sin-1C- 1-cos-D- cos-1-tan-

The correct option is A cos α (1 + cot β)Given, nbsp; a × cos β = cos α and b × sin β = cos α ⇒ a = cos α/cos β and b = nbsp;cos α/sin β Therefore, (a + ...

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Standard X

Mathematics

Trigonometric Ratios

If a ×cosβ=co...

Question

If $a \times c o s β = c o s α$ and $b \times s i n β = c o s α$ , then value of $(a + b) c o s β$ is

c o s α (1 + c o t β)

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s i n α - 1

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1 - c o s β

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c o s α (1 + t a n β)

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Solution

The correct option is A $c o s α (1 + c o t β)$
Given,
$a \times c o s β = c o s α$ and $b \times s i n β = c o s α$
$\Rightarrow a = \frac{c o s α}{c o s β}$ and $b = \frac{c o s α}{s i n β}$

$Therefore, (a + b) c o s β = (\frac{c o s α}{c o s β} + \frac{c o s α}{s i n β}) c o s β = c o s α + \frac{c o s α}{s i n β} \times c o s β = c o s α (1 + \frac{c o s β}{s i n β}) = c o s α (1 + c o t β)$

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If a×cosβ=cosα and b×sinβ=cosα, then value of (a+b)cosβ is

The correct option is A cosα(1+cotβ)Given, a×cosβ=cosα and b×sinβ=cosα ⇒a=cosαcosβ and b=cosαsinβ Therefore, (a+b)cosβ=(cosαcosβ+cosαsinβ)cosβ =cosα+cosαsinβ×cosβ =cosα(1+cosβsinβ) =cosα(1+cotβ)

If $a \times c o s β = c o s α$ and $b \times s i n β = c o s α$ , then value of $(a + b) c o s β$ is