If sin A-sin B and cos A-cos B- A-B- thenA- sin1-2A-BB- cos1-2A-BC- cos1-2A-BD- sin1-2A-B

The correct option is A sinA=sinB⇒ sinA sinB=0 ⇒ 2sinA B/2cosA+B/2=0 (1) and cosA=cosB⇒ cosA cosB=0 ⇒ 2sinA+B/2sinA B/2=0 (2) Equations (1) ...

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Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

If sin A=sin ...

Question

If sin A = sin B and cos A = cos B, A > B, then

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Solution

The correct option is A
$s i n A = s i n B \Rightarrow s i n A - s i n B = 0 \Rightarrow 2 s i n \frac{A - B}{2} c o s \frac{A + B}{2} = 0 (1) a n d c o s A = c o s B \Rightarrow c o s A - c o s B = 0 \Rightarrow 2 s i n \frac{A + B}{2} s i n \frac{A - B}{2} = 0 (2)$
Equations (1) and (2) are simultaneously true if $s i n (\frac{A - B}{2}) = 0$ , while the other factors $s i n (\frac{A + B}{2}) a n d c o s (\frac{A + B}{2})$ cannot both be zero simultaneously.

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Similar questions

Prove that:
(i) $\frac{s i n A + s i n 3 A}{c o s A - c o s 3 A} = c o t A$
(ii) $\frac{s i n 9 A - s i n 7 A}{c o s 7 A - c o s 9 A} = c o t 8 A$
(iii) $\frac{s i n A - s i n B}{c o s A - c o s B} = t a n \frac{A - B}{2}$
(iv) $\frac{s i n A + s i n B}{s i n A - s i n B} t a n (\frac{A + B}{2}) c o t \frac{A + B}{2}$
(v) $\frac{c o s A + c o s B}{c o s B - c o s A} = c o t \frac{A + B}{2} c o t \frac{A - B}{2}$

Q. The biggest among

(sin 1 + cos 1), (\sqrt{sin 1} + \sqrt{cos 1}), (sin 1 - cos 1)

Factorise : 8a³ + b³ + 12a²b + 6ab²

Q. The greatest among (sin1+cos1),

(\sqrt{s i n 1} + \sqrt{c o s 1}), (s i n 1 - c o s - 1)

and 1 is

Q. If

x = sin 1 + cos 1, y = \sqrt{sin 1} + \sqrt{cos 1}

and

z = sin 1 - cos 1,

then which among the following relation between

x, y, z

is correct ?

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If sin A = sin B and cos A = cos B, A > B, then

The correct option is A sinA=sinB⇒sinA−sinB=0⇒2sinA−B2cosA+B2=0(1)andcosA=cosB⇒cosA−cosB=0⇒2sinA+B2sinA−B2=0(2) Equations (1) and (2) are simultaneously true if sin(A−B2)=0, while the other factors sin(A+B2)andcos(A+B2) cannot both be zero simultaneously.