Sources: Visual - various maths sites (credits to original creator) Questions - Dong Zong's Textbook suitable for SUEC (Maths), SPM (Maths and Add Maths) too

1. 𝒑𝒈 𝟐𝟑𝟓 − 𝟐𝟑𝟕

2. 𝒑𝒈 𝟐𝟒𝟎
𝒔𝒊𝒏 𝜽
𝒄𝒐𝒔𝟐
𝑨
𝟏
𝟏
𝒔𝒆𝒄𝟐
𝜶 𝒄𝒐𝒔 𝑨 𝒔𝒊𝒏 𝑨

3. 𝒑𝒈 𝟐𝟑𝟕

4. 𝒑𝒈 𝟐𝟒𝟎

5. 𝒑𝒈 𝟐𝟑𝟕

6. 𝒑𝒈 𝟐𝟑𝟖

7. 𝒑𝒈 𝟐𝟑𝟗

8. 𝒑𝒈 𝟐𝟒𝟎

9. 𝒑𝒈 𝟐𝟒𝟎
𝑠𝑒𝑐 𝛼 + 𝑐𝑜𝑠𝑒𝑐 𝛼 2 + 𝑠𝑒𝑐 𝛼 − 𝑐𝑜𝑠𝑒𝑐 𝛼 2
=
1
𝑐𝑜𝑠 𝛼
+
1
𝑠𝑖𝑛 𝛼
2
+
1
𝑐𝑜𝑠 𝛼
−
1
𝑠𝑖𝑛 𝛼
2
=
𝑠𝑖𝑛 𝛼 + 𝑐𝑜𝑠 𝛼
𝑐𝑜𝑠 𝛼 × 𝑠𝑖𝑛 𝛼
2
+
𝑠𝑖𝑛 𝛼 − 𝑐𝑜𝑠 𝛼
𝑐𝑜𝑠 𝛼 × 𝑠𝑖𝑛 𝛼
2
=
𝑠𝑖𝑛2 𝛼 + 𝑐𝑜𝑠2 𝛼 + 2 𝑠𝑖𝑛 ∝ 𝑐𝑜𝑠 ∝ +𝑠𝑖𝑛2 𝛼 + 𝑐𝑜𝑠2 𝛼 − 2 𝑠𝑖𝑛 ∝ 𝑐𝑜𝑠 ∝
𝑐𝑜𝑠2 𝛼 × 𝑠𝑖𝑛2 𝛼
=
2
𝑐𝑜𝑠2 𝛼 × 𝑠𝑖𝑛2 𝛼
= 2 𝑠𝑒𝑐2
∝ 𝑐𝑜𝑠𝑒𝑐2
∝

10. 𝒑𝒈 𝟐𝟑𝟗

11. 𝒑𝒈 𝟐𝟒𝟎

12. 𝒑𝒈 𝟐𝟒𝟎
tan ∝ + cot 𝛽
cot ∝ + tan 𝛽
=
tan ∝ +
1
tan 𝛽
1
tan ∝
+ tan 𝛽
=
tan ∝ tan 𝛽 + 1
tan 𝛽
×
tan ∝
tan ∝ tan 𝛽 + 1
=
tan ∝
tan 𝛽

13. 𝒑𝒈 𝟐𝟒𝟎

14. 𝒑𝒈 𝟐𝟒𝟎
𝑠𝑖𝑛 𝛼 + 𝑠𝑒𝑐 𝛼 2 + 𝑐𝑜𝑠 𝛼 + 𝑐𝑠𝑐 𝛼 2
= 𝑠𝑖𝑛2
𝛼 + 𝑠𝑒𝑐2
𝛼 + 2 𝑠𝑖𝑛 𝛼 𝑠𝑒𝑐 𝛼 + 𝑐𝑜𝑠2
𝛼 + 𝑐𝑠𝑐2
𝛼
+ 2 𝑐𝑜𝑠 𝛼 𝑐𝑠𝑐 𝛼
= 1 + 𝑠𝑒𝑐2𝛼 + 𝑐𝑠𝑐2𝛼 + 2
𝑠𝑖𝑛 𝛼
𝑐𝑜𝑠 𝛼
+
𝑐𝑜𝑠 𝛼
𝑠𝑖𝑛 𝛼
1 + 𝑠𝑒𝑐 𝛼 𝑐𝑠𝑐 𝛼 2
= 1 + 𝑠𝑒𝑐2 𝛼 𝑐𝑠𝑐2𝛼 + 2 𝑠𝑒𝑐 𝛼 𝑐𝑠𝑐 𝛼
= 1 + (1 + 𝑡𝑎𝑛2
𝛼)(1 + 𝑐𝑜𝑡2
𝛼) +
2
𝑐𝑜𝑠 𝛼 𝑠𝑖𝑛 𝛼
= 1 + 𝑠𝑒𝑐2 𝛼 + 𝑐𝑠𝑐2𝛼 + 2
𝑠𝑖𝑛 𝛼
𝑐𝑜𝑠 𝛼
+
𝑐𝑜𝑠 𝛼
𝑠𝑖𝑛 𝛼
= 1 + 1 + 𝑡𝑎𝑛2 𝛼 + 𝑐𝑜𝑡2𝛼 + 𝑡𝑎𝑛2 𝛼 𝑐𝑜𝑡2 𝛼 +
2 𝑠𝑖𝑛2
𝛼 + 𝑐𝑜𝑠2
𝛼
𝑐𝑜𝑠 𝛼 𝑠𝑖𝑛 𝛼
∴ 𝑠𝑖𝑛 𝛼 + 𝑠𝑒𝑐 𝛼 2
+ 𝑐𝑜𝑠 𝛼 + 𝑐𝑠𝑐 𝛼 2
= 1 + 𝑠𝑒𝑐 𝛼 𝑐𝑠𝑐 𝛼 2

15. 𝒑𝒈 𝟐𝟒𝟏 − 𝟐𝟒𝟐

16. 𝒑𝒈 𝟐𝟒𝟓
𝟔 − 𝟐
𝟒
𝟔 + 𝟐
𝟒
−
𝟔 + 𝟐
𝟒
𝟏
𝟐
𝟏
𝟐
𝟏
𝟐
𝒐𝒓
𝟐
𝟐
𝟑
𝟐
−
𝟏
𝟐

17. 𝒑𝒈 𝟐𝟒𝟑

18. 𝒑𝒈 𝟐𝟒𝟓
𝟑
𝟐
𝑠𝑖𝑛 15 ° = 𝑠𝑖𝑛 (45 ° − 30 °)
= 𝑠𝑖𝑛 45 ° 𝑐𝑜𝑠 30 ° − 𝑐𝑜𝑠 45 ° 𝑠𝑖𝑛 30 °
=
2
2
3
2
−
2
2
1
2
=
6 − 2
4
𝑐𝑜𝑠2 15 ° 𝑠𝑖𝑛2 15 ° =
6 + 2
4
2
−
6 − 2
4
2
=
3
2