Let us fill up the blanks:

(i) The value of (tan 15° x tan 45° x tan 60° tan 75°) is_______.

(ii) The value of (sin 12° x cos 18° x sec 78° cosec 72°) is _______.

(iii) If A and B are complementary to each other, siin A = _______.

(i) The value of tan15° tan45° tan60° tan75° is √3

⇒ we know that tan45° = 1 and tan60° = √3

⇒ tan15°(1)(√3)tan(90 - 15)

⇒ √3 × tan15° cot15°

⇒ √3 × tan15°

= √3 × 1

= √3

(ii) The value of sin12°cos18° × sec78°cosec72° is 1

⇒ sin12°cos18° sec78°cosec72°

⇒ sin12°cos18°sec(90 - 12)°cosec(90 - 18)°

⇒ sin12°cos18°cosec12°sec18°

⇒ sin12°cos18°

= 1

(iii) sinA = cosB

⇒ If A and B are complementary angles then A + B = 90° and A = 90 - B

⇒ sinA = sin(90 - B)

= cosB