If sin A + B = 3 2 = cos A - B , 0 ° < A + B ≤ 90 ° , A > B , find A and B .

Let sin ( A + B ) = 3 2 ⇒ sin ( A + B ) = sin 60 ° ⇒ A + B = 60 ° . . . ( i ) Let cos ( A − B ) = 3 2 ⇒ cos ( A − B ) = cos 30 ° ⇒ A − B = 30 ° . . . ( i i ) Adding (1) and (2), we get 2 A = 90 ° A = 45 ° Subtracting (1) and (2), we have 2 B = 30 ° B = 15 °

If sin A + B = 1 = cos A - B , 0 ° < A + B ≤ 90 ° , A ≥ B , find A and B .

sin ( A + B ) = 1 or sin ( A + B ) = sin 90 ° [As sin 90 ° = 1 ] A + B = 90 ° … ( 1 ) Again, cos ( A - B ) = 1 = cos 0 ° A – B = 0 … ( 2 ) Adding (1) and (2), we get 2 A = 90 ° or A = 45 ° Putting A = 45 ° in (1) we get 45 ° + B = 90 ° or B = 45 ° Hence, A = 45 ° and B = 45 ° .

If cos A + B = 0 , sin A - B = 1 2 , then find A and B , where A and B are acute angles.

Since A and B are acute angles. cos A + B = 0 cos A + B = cos 90 ° sin A - B = 1 2 sin A - B = sin 30 ° Now A + B = 90 ° - - - i A - B = 30 ° - - - i i Add equations i and i i 2 A = 120 ° A = 60 ° From equation i i B = 30 °

If tan A + B = 1 and tan A - B = 1 3 , 0 ° < A + B < 90 ° , A > B , then find the values of A and B .

tan ( A + B ) = 1 ⇒ A + B = 45 ° tan ( A - B ) = 1 3 ⇒ A - B = 30 ° A + B = 45 ° . . . . . . . . ( 1 ) A - B = 30 ° . . . . . . . . . . ( 2 ) Adding ( 1 ) and ( 2 ) 2 A = 75 ° A = 37 . 5 ° Put A = 37 . 5 ° in ( 1 ) we get B = 45 ° - 37 . 5 ° B = 7 . 5 ° Hence, the required answers are A = 37 . 5 ° and B = 7 . 5 ° .

If sin ( A + 2 B ) = 3 2 and cos ( A + 4 B ) = 0 , A > B and A + 4 B ≤ 90 ° , then find A and B .

sin ( A + 2 B ) = 3 2 sin ( A + 2 B ) = sin 60 ° On comparing L H S and R H S . A + 2 B = 60 ° - - - 1 cos ( A + 4 B ) = 0 The range lies as A + 4 B ≤ 90 ° , hence the value will be cos 90 ° = 0 . cos ( A + 4 B ) = cos 90 ° On comparing L H S and R H S . A + 4 B = 90 ° - - - 2 On subtracting equation 1 by equation 2 A + 4 B - A - 2 B = 90 ° - 60 ° 2 B = 30 ° B = 15 ° Put value of B in equation 1 A = 30 ° Hence, the values are A = 30 ° , B = 15 ° .

E M B I B E

CBSE Syllabus Standard Mathematics for Class X>Chapter 10 - Introduction to Trigonometry>Exercise 10.2>Q 16

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Find the value of $\cos 60 °$ geometrically. Hence, find $\cos e c 60 °$ .

Important Questions on Introduction to Trigonometry

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CBSE Syllabus Standard Mathematics for Class X>Chapter 10 - Introduction to Trigonometry>Exercise 10.2>Q 17

In the adjoining figure, $A B C$ is a right angled triangle at $B$ . If $A C = 10 c m$ and $∠ C = 30 °,$ then find the lengths of the sides $A B$ and $B C$ .