20. If A and B are complementary an...
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20. If A and B are complementary angles, then the value of sin A cos B + cos A sin B - tan A tan B + sec2 A - cot2 B is (1) 2 (2) O (3) 1 (4)-1

11th - 12th Class
Maths
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20. (3) ( A+B=90^{circ} Rightarrow A=90^{circ}-B ) ( Rightarrow sin A=sin left(90^{circ}-Bright)=cos B ) Similarly, ( Rightarrow cos A=sin B, tan A=cot B ) ( therefore sin A cdot cos B+cos A cdot sin B- ) ( tan A cdot tan B+sec ^{2} A-cot ^{2} B= ) ( cos ^{2} B+sin ^{2} B-cot B . tan B+ ) ( sec ^{2} A-tan ^{2} A=1-1+1=1 ) ( left[because tan B cdot cot B=1, sec ^{2} A-tan ^{2} Aright. ) ( =1} )
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