plz get me all que answers with explanation on a page
Answers
(10) sin30°.tan45° = (1/2).(1)= 1/2
therefore options (c) is correct answer.
(11) If cosA= 4/5 then tanA= 3/4
(12) {tan²60°-sin²30°}/{ tan²45°+cos²30°}
= [(√3)²-(1/2)²]/[(1)²+(√3/2)²
= [3-1/4]/[1+3/4]
= (11/4)/(7/4)
=11/7
option (D).is correct answer.
(13)X=rsin∅ y= rcos∅
then x²+y²= r²(sin²∅+cos²∅)= r²×1=r²
option (b) is right answer.
(14)if 3sec∅-5=0 then sec∅= 5/3 and then
cot∅= 3/4
option(c) is correct answer.
(15)Given
a+b=90° and a= 2b then
3 b=90°
b= 30° then a= 60°
therefore,
cos²a+sin²b= cos²60°+sin²30°
=(1/2)²+(1/2)²
= 1/4+1/4= 2/4= 1/2
therefore option (b) is correct answer.
(16) tanx+sinx= m and tanx-sinx=n then
m²-n²= (tanx+sinx)²-(tanx-sinx)²
=(tanx+sinx+tanx-sinx)(tanx+sinx-tanx+sinx)
= (2tanx)(2sinx)
=4 tanx.sinx=4√mn
option (a) is correct answer.
(17) sec∅+tan∅=x then sec∅-tan∅=1/x
therefore,
sec∅= 1/2(x+1/x)
option (c). is correct answer.
(18) √1+cos∅/1-cos∅= √(1+cos∅)²/1-cos²∅
= √(1+cos∅)²/sin²∅
= (1+cos∅)/sin∅
= cosec∅+cot∅
option (b).is correct answer.
(19) (sin∅/1-cot∅)+(cos∅/1-tan∅)
= [sin²∅/sin∅-cos∅]+[cos²∅/cos∅-sin∅]
= [sin²∅/sin∅-cos∅]-[cos²∅/sin∅-cos∅]
= (sin²∅-cos²∅)/(sin∅-cos∅)
= (sin∅-cos∅)(sin∅+cos∅)/(sin∅-cos∅)
= sin∅+cos∅
option (c) is correct answer.
(20) if sin∅= a/b then tan∅= a/√b²-a²
option (c) is correct answer.