1. . Evaluate (111) (1) cos12° - sin78° (1) 1 cosec 31° – sec 599 tan 36° cot 54° (iv) sin 150 sec 750 (vi) tan 26° tan64°
Answers
Answer:
cos12°-sin78°
sin(90-12)°-sin78°
cos12°-sin78°
hence proved
may this help u
Given :
(i) cos12° - sin78°
(ii) cosec 31° – sec 59°
iii) tan 36° - cot 54°
(iv) sin 150° sec 750 °
(vi) tan 26° tan64°
To Find : Evaluate
Solution:
Sin( 90° - x) = cosx
cos(90° - x) = sinx
Tan (90° - x) = cotx
cot (90° - x) = tanx
tanx = 1/cotx , cotx = 1/tanx , cotxtanx = 1
cosec(90° - x) = secx , sec(90° - x) = cosec x
sinx = 1/cosecx , cosecx = 1/sinx ,
cosx = 1/secx , secx = 1/cosx
(i) cos12° - sin78°
= cos12° - sin(90°-12°)
= cos12° - cos12°
= 0
(ii) cosec 31° – sec 59°
= cosec 31° – sec (90° - 31°)
= cosec 31° – cosec 31°
= 0
iii) tan 36° - cot 54°
= tan 36° - cot (90° - 36°)
= tan 36° - tan 36°
= 0
(iv) sin 150° sec 750 °
= sin ( 180° - 30°) sec( 2 * 360° + 30°)
= sin 30° sec 30°
= sin 30° /cos 30°
= tan 30°
= 1/√3
(vi) tan 26° tan64°
= tan 26° tan ( 90° - 26°)
= tan 26° cot 26°
= 1
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