TOPIC 27 | proving of identities set 1 of 13 get the full set details at the bottom of page
Question 1:
2 + sin 2A
Prove the identity sec 2 A + tan A =
2(1 + sin A)(1 − sin A)
Question 2:
Prove the identity cot x +
1
≡ cos ec x
cos ec x + cot x
Question 3:
1 − cos x
sin x
Show that
+
≡ 2 cos ec x
sin x
1 − cos x
Question 4:
1 + sin x
cos x
2sec x
+
=
cos x
1 + sin x
Hence, find all the values of x (in radians) between 0 and 6 for which
1 + sin x
cos x
+
=
3
cos x
1 + sin x
Prove the identity
Question 5:
Prove the identity
cos ec A − sin A
≡ cot 3 A
sec A − cos A
Question 6:
Prove the identity (sinθ + cosθ )(tanθ + cot θ ) ≡ sec θ + cos ecθ
Question 7:
cos( A + B) 1
Given that
= , show that 3cos Acos B = 5 sin Asin B
cos( A − B) 4
Question 8:
Prove that (1 + cosθ )(cos ec θ − cot θ ) =
sinθ . Hence or otherwise, solve the
equation 4(1 + cosθ )(cos ec θ − cot θ )=
+ 3 tan 35° for 0° ≤ θ ≤ 360°
Question 9:
Prove the identity
cosθ
sinθ
=
cosθ + cot θ sinθ + 1
Page
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TOPIC 27 | proving of identities set 1 of 13 get the full set details at the bottom of page
Question 10:
Prove the identity tan 2 x − sin 2 x =
tan 2 x sin 2 x
Question 11:
(sin x + cos x)2
Prove the identity
= 2 + sec x cos ec x
sin x cos x
Question 12:
Prove the identity
1 + 2sin x cos x 1 + tan x
=
2
1 − 2sin x
1 − tan x
Question 13:
1 − cos x
sin x
2
Prove
+
≡
sin x
1 − cos x sin x
Question 14:
Prove (sec x + tan x)2 ≡
1 + sin x
1 − sin x
Question 15:
Given (sin x cos x)( 5 tan x + 2cot x) =
a + b sin 2 x , find the values of the
constants a and b
Question 16:
Prove the identity
Question 17:
Prove the identity
1 − cos x
sin x
+
≡ 2cos ecx
sin x
1 − cos x
1 + cos x
sin x
2
+
=
sin x
1 + cos x sin x
Question 18:
1 + sin x
cos x
2
Prove
+
=
cos x
1 + sin x cos x
Question 19:
Prove the following identity: cos x=
cot x cos ec x − sin x
Page
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|2
TOPIC 27 | proving of identities set 1 of 13 get the full set details at the bottom of page
Question 20:
sin2 x
Prove the following identity: cos x= 1 −
1 + cos x
Page
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BOOK now to get FULL PRACTICE SET free M: 8429 5372 E: [email protected]
|3